View source for 4.7

{{DISPLAYTITLE:Elementary Functions - 4.7 Derivatives and Differential Equations}}

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! scope="col" style="position: sticky; top: 0;" | DLMF 
! scope="col" style="position: sticky; top: 0;" | Formula 
! scope="col" style="position: sticky; top: 0;" | Constraints 
! scope="col" style="position: sticky; top: 0;" | Maple
! scope="col" style="position: sticky; top: 0;" | Mathematica
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Maple
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Maple
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/4.7.E1 4.7.E1] || <math qid="Q1577">\deriv{}{z}\ln@@{z} = \frac{1}{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\ln@@{z} = \frac{1}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(ln(z), z) = (1)/(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Log[z], z] == Divide[1,z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
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| [https://dlmf.nist.gov/4.7.E2 4.7.E2] || <math qid="Q1578">\deriv{}{z}\Ln@@{z} = \frac{1}{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\Ln@@{z} = \frac{1}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(ln(z), z) = (1)/(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Log[z], z] == Divide[1,z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
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| [https://dlmf.nist.gov/4.7.E3 4.7.E3] || <math qid="Q1579">\deriv[n]{}{z}\ln@@{z} = (-1)^{n-1}(n-1)!z^{-n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[n]{}{z}\ln@@{z} = (-1)^{n-1}(n-1)!z^{-n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(ln(z), [z$(n)]) = (- 1)^(n - 1)*factorial(n - 1)*(z)^(- n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Log[z], {z, n}] == (- 1)^(n - 1)*(n - 1)!*(z)^(- n)</syntaxhighlight> || Failure || Failure || Successful [Tested: 21] || Successful [Tested: 21]
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| [https://dlmf.nist.gov/4.7.E4 4.7.E4] || <math qid="Q1580">\deriv[n]{}{z}\Ln@@{z} = (-1)^{n-1}(n-1)!z^{-n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[n]{}{z}\Ln@@{z} = (-1)^{n-1}(n-1)!z^{-n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(ln(z), [z$(n)]) = (- 1)^(n - 1)*factorial(n - 1)*(z)^(- n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Log[z], {z, n}] == (- 1)^(n - 1)*(n - 1)!*(z)^(- n)</syntaxhighlight> || Failure || Failure || Successful [Tested: 21] || Successful [Tested: 21]
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| [https://dlmf.nist.gov/4.7.E7 4.7.E7] || <math qid="Q1583">\deriv{}{z}e^{z} = e^{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}e^{z} = e^{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(exp(z), z) = exp(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Exp[z], z] == Exp[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
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| [https://dlmf.nist.gov/4.7.E8 4.7.E8] || <math qid="Q1584">\deriv{}{z}e^{az} = ae^{az}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}e^{az} = ae^{az}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(exp(a*z), z) = a*exp(a*z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Exp[a*z], z] == a*Exp[a*z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 42]
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| [https://dlmf.nist.gov/4.7.E9 4.7.E9] || <math qid="Q1585">\deriv{}{z}a^{z} = a^{z}\ln@@{a}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}a^{z} = a^{z}\ln@@{a}</syntaxhighlight> || <math>a \neq 0</math> || <syntaxhighlight lang=mathematica>diff((a)^(z), z) = (a)^(z)* ln(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[(a)^(z), z] == (a)^(z)* Log[a]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 42]
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| [https://dlmf.nist.gov/4.7.E10 4.7.E10] || <math qid="Q1586">\deriv{}{z}z^{a} = az^{a-1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}z^{a} = az^{a-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff((z)^(a), z) = a*(z)^(a - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[(z)^(a), z] == a*(z)^(a - 1)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 42]
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| [https://dlmf.nist.gov/4.7.E14 4.7.E14] || <math qid="Q1590">\deriv[2]{w}{z} = aw</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z} = aw</syntaxhighlight> || <math>a \neq 0</math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)]) = a*w</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}] == a*w</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.299038106+.7500000000*I
Test Values: {a = -1.5, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.299038106+.7500000000*I
Test Values: {a = -1.5, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.299038106+.7500000000*I
Test Values: {a = -1.5, w = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.299038106+.7500000000*I
Test Values: {a = -1.5, w = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.299038105676658, 0.7499999999999999]
Test Values: {Rule[a, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.299038105676658, 0.7499999999999999]
Test Values: {Rule[a, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| [https://dlmf.nist.gov/4.7.E15 4.7.E15] || <math qid="Q1591">w = Ae^{\sqrt{a}z}+Be^{-\sqrt{a}z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w = Ae^{\sqrt{a}z}+Be^{-\sqrt{a}z}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w = A*exp(sqrt(a)*z)+ B*exp(-sqrt(a)*z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w == A*Exp[Sqrt[a]*z]+ B*Exp[-Sqrt[a]*z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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