SEARCH WEB myHandbook Google

Normal Density High Derivatives

This table list the normal density function and its higher derivatives (from seventh derivative). For lower derivative, see Derivatives of Normal Density Function
Normal Density FunctionDerivative of Normal Density Function

How To Use:

  • You need to find the value of ninth derivative of the Normal Density Function at Z = 0.10
  • Find the row with Z = 0.10
  • Find the column φ(9)(x), the number inside the cell is 37.0133546.
    See How To Read Numbers in Tables.
  • The result is -37.0133546
Z φ(7)(x) φ(8)(x) φ(9)(x) φ(10)(x) φ(11)(x) φ(12)(x) φ(13)(x)
0.00041.88893940377.00045504147.005000
0.02.83727623241.81356707.53448120376.17141382.86824024136.228181077.14345
0.041.6715397841.587781115.0358295373.688597165.3058384103.962332147.82855
0.062.4997911941.212574522.4710840369.564906246.8847344050.400883205.64087
0.083.3190574740.689595929.8076274363.821753327.1820143975.864734244.25335
0.104.1264050540.021141737.0133546356.488940405.7824403880.800095257.46929
0.124.9189527039.210143644.0568389347.604471482.2809253765.775486239.26416
0.145.6938840538.260153950.9074939337.214336556.2849463631.477807183.82625
0.166.4484598137.175326957.5357308325.372225627.4168643478.707778085.59561
0.187.1800296535.960397363.9131087312.139216695.3161463308.374478939.30116
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
0.207.8860435134.620656270.0124793297.583410759.6414753121.489219739.99555
0.228.5640625133.161923375.8081232281.779523820.0727272919.1587510483.0877
0.249.2117691931.590517681.2758777264.808448876.3128052702.5778511164.3723
0.269.8269772029.913224586.3932560246.756774928.0893212473.0212911780.0574
0.2810.407640328.137261691.1395555227.716279975.1561132231.8353612326.7873
0.3010.951860526.270242095.4959569207.7833911017.294591980.4289212801.6637
0.3211.457896024.320135499.4456112187.0586231054.314871720.2641013202.2630
0.3411.924167222.2952284102.973715165.6459921086.056791452.8466013526.6493
0.3612.349263520.2040823106.067577143.6524121112.390641179.7159113773.3854
0.3812.731947518.0554909108.716667121.1870851133.21776902.43518513941.5385
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
0.4013.071160015.8584368110.91265598.36086901148.47089622.58120214030.6832
0.4213.366022713.6220466112.64944175.28565381158.11439341.73414914040.9010
0.4413.615841111.3555467113.92316952.07372551162.1441361.467561613972.7753
0.4613.82010579.06821810114.73222628.83713891160.58734216.66165113827.3838
0.4813.97849296.76935178115.0772325.687094601153.50213491.12298113606.2865
0.5014.09086464.46820409114.96101917.26667261140.97685760.42182513311.5113
0.5214.15726712.17395293114.38859239.91649161123.129351023.1086712945.5357
0.5414.1779291.104345279113.36708662.15733421100.105901277.7878612511.2654
0.5614.15325902.35779758111.90570583.88737311072.080121523.1259712012.0109
0.5814.08384084.57771524110.015652105.0085151039.251581757.8595811451.4604
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
0.6013.97043036.75565293107.710050125.4269071001.844361980.8025910833.6508
0.6213.81394918.88344625105.003856145.053407960.1054472190.8528510162.9366
0.6413.615479110.9532474101.913755163.804030914.3029672386.998239443.95674
0.6613.376255912.957558898.4580581181.600348864.7243512568.321898681.59976
0.6813.097660914.889264394.6565875198.369858811.6743722734.007017880.96769
0.7012.781214116.741658390.5305522214.046311755.4731052883.340597047.33884
0.7212.428565218.508472186.1024217228.569993696.4538223015.716676186.12986
0.7412.041484620.183898281.3957921241.887970634.9608233130.638685302.85725
0.7611.621854121.762610976.4352489253.954287571.3472313227.721054403.09877
0.7811.171657223.239784871.2462255264.730119505.9727623306.690073492.45489
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
0.8010.692968524.611110865.8548595274.183885439.2014873367.383932576.51070
0.8210.187943725.872808260.2878473282.291308371.3996003409.752061660.79851
0.849.6588087927.021634454.5722974289.035440302.9332053433.85373750.761329
0.869.1078489528.054892348.7355843294.406633234.1661383439.85584148.282363
0.888.5373980028.970433342.8052027298.402478165.4578463428.030171031.17240
0.907.9498271829.766659136.8086242301.02769497.16131783398.749821892.93902
0.927.3475342030.442519130.7731560302.29397529.62110253352.485142728.83310
0.946.7329323530.997506224.7258030302.21981136.82859243289.799043534.35421
0.966.1084396931.431649218.6931343300.830252101.8656993211.341704305.27643
0.985.4764684231.745503012.7011545298.156658165.1819813117.844905037.67177
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
1.004.8394144931.94013566.77518029294.236401226.4845983010.115815727.93099
1.024.1996474732.0171139.939723607289.112543285.4975582889.030466372.78176
1.043.5595007531.97848564.78161900282.833486341.9630162755.526816969.30408
1.062.9212621231.826760610.3662693275.452600395.6424492610.597617514.94285
1.082.2871647331.564889415.7927628267.027821446.3176752455.282948007.51768
1.101.6593784931.196239921.0408360257.621239493.7917232290.662748445.22968
1.121.0400020030.724572326.0915050247.298665537.8895552117.849028826.66556
1.14.43105494330.154013630.9271359236.129187578.4586331937.978229150.79876
1.16.16552897029.489029035.5315054224.184714615.3693221752.203459416.98786
1.18.74790848328.734393839.8898526211.539518648.5151581561.686829624.97234
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
1.201.3143407027.895163743.9889221198.269767677.8129411367.591919774.86558
1.221.8631863926.976643947.8169967184.453059703.2026991171.076369867.14555
1.242.3929146525.984358551.3639217170.167964724.647493973.2847119902.64295
1.262.9021070024.924018954.6211198155.493559742.133083775.3414689882.52725
1.283.3894607923.801492257.5815964140.508987755.667467578.3444969808.29056
1.303.8537920322.622769760.2399368125.293009765.280280383.3587379681.72971
1.324.2940374921.393935062.5922941109.923587771.022075191.4103159504.92652
1.344.7092563120.121133464.636369394.4774662772.9634983.481041479280.22657
1.365.0986308918.810541066.371382879.0297881771.194340179.4966339010.21666
1.385.4614671917.468334267.798038763.6537142765.822512356.6442118697.70114
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
1.405.7971944916.100661168.918481548.4200762756.972922527.1412538345.67731
1.426.1053644914.713613169.736246533.3970476744.786272690.2289837957.31011
1.446.3856499213.313197070.256203018.6498404729.417800845.2133877535.90632
1.466.6378425911.905309770.48449284.24042741711.035952991.4677897084.88845
1.486.8618509410.495713070.42846279.77270814689.8210191128.434906607.76858
1.507.057697119.0900103270.096592323.3347956665.9637301255.628356108.12224
1.527.225513517.6936248569.498417936.3949715639.6638221372.633705589.56265
1.547.365539086.3117790768.644452448.9064451611.1285991479.108945055.71542
1.567.478115024.9494761667.546102960.8266351580.5714791574.784494510.19393
1.587.563680253.6114829166.215585072.1172781548.2105501659.462733956.57549
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
1.607.622766562.3023144464.665835682.7445069514.2671451733.017013398.37852
1.627.655993391.0262206862.910424692.6789017478.9644251795.390292839.04084
1.647.66406243.21282545260.9634657101.895513442.5260161846.593312281.89917
1.667.647751991.4111380058.8395268110.373857405.1746671886.702371730.17007
1.687.607911142.5653261556.5535412118.097885367.1309661915.856751186.93225
1.707.545453773.6723006954.1207190125.055929328.6121111934.25580655.110471
1.727.461352494.7292786551.5564607131.240620289.8307401942.15569137.461085
1.747.356632505.7337862548.8762719136.648789250.9938261939.86594363.440827
1.767.232365346.6836601946.0956808141.281340212.3016501927.74564845.212534
1.787.089662747.5770472943.2301577145.143106173.9468481906.199561305.67304
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
1.806.929670398.4124025740.2950385148.242692136.1135391875.673991742.85071
1.826.753561859.1884857737.3054507150.59229298.97653501836.652512154.98914
1.846.562532449.9043565434.2762435152.20749762.70064061789.651642540.55134
1.866.3577933810.559368231.2219222153.10708927.44003681735.216452898.22215
1.886.1405659111.153160128.1565863153.3128236.662244751673.916033226.90908
1.905.9120757211.685649225.0938722152.84920039.47475811606.339163525.74150
1.925.6735474512.157020122.0469011151.74323170.87799221533.089793794.06831
1.945.4261994812.567714119.0282306150.024194100.7646311454.782754031.45410
1.965.1712388812.918417816.0498122147.723392129.0397271372.039454237.67403
1.984.9098566313.210050413.1229531144.873901155.6207931285.483744412.70732
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
2.004.6432231213.443750710.2582836141.510323180.4378101195.737944556.72959
2.024.3724839013.62086277.46572851137.668536203.4331571103.418924670.10410
2.044.0987556713.74292204.75448439133.385447224.5614671009.134524753.37202
2.063.8231226613.81164072.13300149128.698749243.789408913.4800584807.24182
2.083.5466331913.8288919.391029728123.646686261.095404817.0351034832.57786
2.103.2702966613.79669552.81068721118.267816276.469286720.3604764830.38843
2.122.9950807113.71720155.11982137112.600792289.911892623.9954984801.81316
2.142.7219088413.59267557.31305478106.684142301.434611528.4554924748.11009
2.162.4516581613.42548289.38577765100.556066311.058879434.2295464670.64236
2.182.1851576513.218073611.334139294.2542388318.815633341.7785474570.86483
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
2.201.9231865412.972967213.155035587.8156267324.744734251.5334804450.31046
2.221.6664731212.692737914.846093281.2763143328.894350163.8940014310.57688
2.241.4156937512.380000316.405650674.6713452331.32032079.22728184153.31295
2.261.1714722312.037395217.832735368.0345749332.0854922.132888163980.20558
2.28.93437937211.667576219.127038861.3985375331.25905479.88672983792.96690
2.30.70493291411.273196820.288889354.7943257328.915842153.7688543593.32174
2.32.48359762710.856897621.319221448.2514846325.135658223.5483963382.99562
2.34.27078569410.421294822.219544241.7979195320.002574289.0289093163.70324
2.36.0668573129.9689689822.991908335.4598172313.604252350.0480442937.13763
2.38.1278784879.5024545823.638869829.2615811306.031261406.4770092704.95985
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
2.40.3131628189.0242301224.163454823.2257795297.376419458.2198322468.78943
2.42.4887857328.5367092524.569122317.3731074287.734143505.2124432230.19560
2.44.6545848338.0422324124.859725711.7223609277.199818547.4215861990.68914
2.46.8104437407.5430593225.03947586.29042329265.869200584.8435751751.71520
2.48.9562904007.0413622625.11290161.09226436253.837832617.5029151514.64675
2.501.092095286.5392200725.08481253.85905049241.200498645.4508011280.77898
2.521.217869466.0386129024.96026028.55233957228.050706668.7635151051.32442
2.541.333662575.5414177424.744501612.9782745214.480199687.540725827.408949
2.561.439560745.0494047424.442962117.1293402200.578510701.903727610.068573
2.581.535684404.5642341124.061199220.9997870186.432542711.993614400.246974
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
2.601.622186074.0874539023.604868724.5855735172.126196717.969417198.793865
2.621.699248083.6204983523.079690327.8843035157.740028720.0062126.46406177
2.641.767080323.1646869322.491416130.8951560143.350949718.293221176.082720
2.661.825917912.7212239921.845799133.6188096129.031957713.031911348.281400
2.681.876018892.2911990721.148564636.0573616114.851917704.434116509.660424
2.701.917661981.8755877020.405382738.2142439100.875368692.720177659.840060
2.721.951144271.4752528019.621841840.094134487.1623720678.117130798.530130
2.741.976778981.0909465118.803425341.702866673.7683979660.856943925.527249
2.761.99489330.72331255217.955489143.047336860.7442409641.1748101040.71158
2.782.00582624.37288898417.083241344.135409948.1359733619.3075151144.04321
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
2.802.00992652.04011132416.191723944.975825035.9849290595.4918761235.55810
2.822.00755060.27468394515.285796045.578100324.3277174569.9632671315.36380
2.841.99906068.57125557314.370119645.952439813.1962669542.9542351383.63483
2.861.98482288.84945346413.449146246.10963922.61789350514.6932071440.60785
2.881.965205471.1092143612.527106446.06099567.38460361485.4032941486.57673
2.901.940577111.3505573311.608000645.818217816.7928254455.3012031521.88739
2.921.911305331.5735790910.695591745.393339625.5926344424.5962431546.93264
2.941.877754981.778449179.7933992544.798636333.7739982393.4894451562.14695
2.961.840286811.965405048.9046955544.046544241.3308152362.1727731568.00119
2.981.799256212.134747128.0325032843.149583848.2607271330.8284561564.99752
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
3.001.755011972.286833787.1795944342.120287354.5649176299.6284071553.66423
3.021.707895172.422076326.3484908340.971129260.2479019268.7337581534.55077
3.041.658238162.540933995.5414659439.714462465.3173063238.2944751508.22288
3.061.606363702.643909064.7605478738.362458069.7836428208.4490911475.25793
3.081.552584092.731541924.0075235836.927049973.6600779179.3245091436.24042
3.101.497200482.804406353.2839441835.419884176.9621990151.0359091391.75770
3.121.440502282.863104842.5911311133.852272779.7077796123.6867271342.39594
3.141.382766562.908264081.9301832532.235152181.916545197.36872141288.73633
3.161.324257672.940530551.3019848230.579047083.609940372.16210561231.35154
3.181.265226872.96056637.70721395628.894037784.810900248.13575161170.80249
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
3.201.205912062.96904521.14635184127.189732885.543626425.34745581107.63538
3.221.146537572.96664850.38030759025.475246085.83336813.844260991042.37894
3.241.087314062.95406174.87264757223.759177585.706210816.3371706975.542097
3.261.028438462.931971091.3307180822.049598985.188873135.1701387907.611826
3.28.9700940142.901060141.7547251320.354042884.308511752.6374476839.051312
3.30.9124503352.862006862.1450199718.679495983.092536168.7309145770.298415
3.32.8556635562.815480882.5020880717.032395581.568433883.4508495701.764385
3.34.7998765242.762140822.8265381515.418630079.763605696.8055129633.832854
3.36.7452190442.702632023.1190912313.843541677.7052122108.810555566.859082
3.38.6918081652.637584353.3805698012.311933375.4200324119.488444501.169450
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
3.40.6397485082.567610323.6118870310.828077072.9343321128.867882437.061186
3.42.5891326342.493303343.814036359.3957257470.2737456136.983227374.802311
3.44.5400414372.415236243.988081188.0181269367.4631685143.873903314.631794
3.46.4925445742.333959984.135144946.6980383264.5266620149.583829256.759896
3.48.4467009082.250002504.256401455.4377454861.4873688154.160843201.368691
3.50.4025589822.163867884.353065714.2390809158.3674403157.656151148.612755
3.52.3601575052.076035514.426384973.1034445455.1879745160.12378098.6199872
3.54.3195258461.986959644.477630362.0318253051.9689651161.62005851.4925752
3.56.2806845461.897068884.508088851.0248236448.7292606162.2031087.30806368
3.58.2436458321.806766034.51905573.08267476045.4865329161.93236633.8794735
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
3.60.2084141341.716427954.51182755.79472762242.2572561160.86812672.0381797
3.62.1749866041.626405624.487695511.6078071839.0566931159.071108107.157094
3.64.1433536301.537024294.447939362.3572806935.8988919156.602054139.244774
3.66.1134993541.448583784.393821813.0441337732.7966884153.521351168.327884
3.68.0854021701.361358884.326583333.6695967129.7617174149.888684194.449748
3.70.0590352211.275599824.247437574.2351206226.8044295145.762716217.668895
3.72.0343668911.191532874.157567154.7423539623.9341147141.200800238.057601
3.74.0113612681.109360974.058119905.1931196621.1589315136.258720255.700435
3.76.0100213891.029264513.950205675.5893927418.4859400130.990455270.692829
3.78.029824211.9514020583.834893465.9332787715.9211409125.447979283.139670
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
3.80.048093287.8759112443.713209026.2269930913.4695165119.681087293.153931
3.82.064877259.8029096313.586132876.4728408611.1350766113.737242300.855346
3.84.080226927.7324956393.454598676.673198148.92090583107.661458306.369128
3.86.094194874.6647494903.319492026.830493816.82921416101.496199309.824756
3.88.106835116.5997341853.181649576.947192654.8613881995.2813053311.354806
3.90.118202762.5374964883.041858407.025779383.0180444589.0539465311.093858
3.92.128353706.4780679142.900855877.068743791.2990830682.8485873309.177465
3.94.137344325.4214657332.759329597.07856697.29625799376.6969802305.741198
3.96.145231207.3676939572.617917737.057708591.7693487470.6281735300.919752
3.98.152070900.3167443222.477209607.008595303.1221133264.6685373294.846138
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
4.00.157919666.2685972632.337746386.933610174.3569768358.8418045287.650940
4.02.162833277.2232228642.200022126.835083175.4768130953.1691262279.461644
4.04.166866805.1805817882.064484866.715282766.4848937047.6691398270.402049
4.06.170074453.1406261901.931537966.576408397.3848385042.3580480260.591737
4.08.172509387.1033005911.801541516.420584048.1805678037.2497079250.145622
4.10.174223596.0685427281.674813966.249852668.8762563632.3557282239.173562
4.12.175267761.0362843751.551633726.066171539.4762895527.6855739227.780039
4.14.1756911463z645212181.432240955.871408459.9852214623.2466762216.063897
4.16.175541502.0210318781.316839405.6673388110.407735519.0445474204.118143
4.18.174864983.0462491971.205598225.4556433310.748606915.0828997192.029804
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
4.20.173706082.0692844601.098653925.2379066111.012668511.3637648179.879835
4.22.172107572.090224712.9961122915.0156162711.20477787.88761685167.743076
4.24.170110468.109158822.8980503364.7901628211.32978704.65349413155.688259
4.26.167753992.126176929.8045182194.5628399811.39251611.65912110143.778049
4.28.165075558.141369923.7155411924.3348456111.39772731.09897110132.069131
4.30.162110755.154828964.6311214954.1072831111.35010243.62532617120.612326
4.32.158893352.166645043.5512402313.8811631911.25422275.92544685109.452742
4.34.155455303.176908579.4758591963.6574061211.11455068.0056822898.6299460
4.36.151826763.185709045.4049226663.4368442310.93541429.8731192988.1781699
4.38.148036107.193134642.3383591263.2202247510.720993111.535477778.1265252
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
4.40.144109965.199271995.2760829413.0082129010.475307313.001010468.4992422
4.42.140073250.204205890.2179959662.8013951810.202207014.278408159.3159205
4.44.135949200.208019036.1639890822.600282859.9053650415.376709450.5917907
4.46.131759423.210791865.1139436702.405315559.5882706516.305216142.3379842
4.48.127523941.212602350.0677330012.216864999.2542251517.073413834.5618081
4.50.123261242.213525861.0252235612.035238778.9063388717.690898427.2670236
4.52.118988335.213635041.0137237071.860684218.5475297118.167307920.4541246
4.54.114720803.212999705.0492522361.693392198.1805229118.512259914.1206150
4.56.110472863.211686765.0815087451.533501017.8078520718.73529438.26128290
4.58.106257423.209760176.1106422221.381100207.4318611518.84582182.86846975
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
4.60.102086140.207280895.1368029941.236234287.0547076218.85307802.06766736
4.62.097969485.204306869.1601418561.098906446.6783663218.76608156.55890086
4.64.093916797.200893030.180809284.9690821926.3046342118.593598610.6186871
4.66.089936349.197091310.198954716.8466928145.9351356718.344111314.2619305
4.68.086035403.192950669.214725905.7316387865.5713285718.025791017.5047593
4.70.082220274.188517132.228268328.6237930435.2145105817.646476320.3643115
4.72.078496382.183833842.239724676.5230041074.8658261517.213654222.8585343
4.74.074868316.178941121.249234389.4290990874.5262735716.734446825.0059948
4.76.071339883.173876538.256933260.3418865254.1967124616.215599526.8257042
4.78.067914167.168674984.262953088.2611590953.8778713515.663475028.3369543
Zφ(7)(x)φ(8)(x)φ(9)(x) φ(10)(x)φ(11)(x)φ(12)(x)φ(13)(x)
4.80.064593581.163368757.267421389.1866961453.5703553915.084048329.5591670
4.82.061379915.157987651.270461155.1182660913.2746541014.482905830.5117566
4.84.058274391.152559045.272190652.0556286492.9911491813.865246931.2140048
4.86.055277702.147108003.2727232733z146308302.7201221513.235887531.6849477
4.88.052390067.141657369.272167423.0532607022.4617620112.599266331.9432755
4.90.049611266.136227872.270626443.1000187192.2161727011.959452132.0072431
4.92.046940686.130838223.268198566.1419929391.9833804011.320153931.8945924
4.94.044377359.125505220.264976913.1794389671.7633406310.684731431.6224853
4.96.041920000.120243850.261049501.2126108721.5559450910.056207231.2074468
4.98.039567039.115067391.256499296.2417599731.361028299.4372805930.6653179
5.00.037316660.109987510.251404270.2671337621.178373898.8303408230.0112175


Copyright © 2006 myhandbook.info
Contact :