Elementary Functions - 4.7 Derivatives and Differential Equations

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
4.7.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\ln@@{z} = \frac{1}{z}}
\deriv{}{z}\ln@@{z} = \frac{1}{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
diff(ln(z), z) = (1)/(z)

D[Log[z], z] == Divide[1,z]
Successful Successful - Successful [Tested: 7]
4.7.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\Ln@@{z} = \frac{1}{z}}
\deriv{}{z}\Ln@@{z} = \frac{1}{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
diff(ln(z), z) = (1)/(z)

D[Log[z], z] == Divide[1,z]
Successful Successful - Successful [Tested: 7]
4.7.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\ln@@{z} = (-1)^{n-1}(n-1)!z^{-n}}
\deriv[n]{}{z}\ln@@{z} = (-1)^{n-1}(n-1)!z^{-n}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
diff(ln(z), [z$(n)]) = (- 1)^(n - 1)*factorial(n - 1)*(z)^(- n)

D[Log[z], {z, n}] == (- 1)^(n - 1)*(n - 1)!*(z)^(- n)
Failure Failure Successful [Tested: 21] Successful [Tested: 21]
4.7.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[n]{}{z}\Ln@@{z} = (-1)^{n-1}(n-1)!z^{-n}}
\deriv[n]{}{z}\Ln@@{z} = (-1)^{n-1}(n-1)!z^{-n}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
diff(ln(z), [z$(n)]) = (- 1)^(n - 1)*factorial(n - 1)*(z)^(- n)

D[Log[z], {z, n}] == (- 1)^(n - 1)*(n - 1)!*(z)^(- n)
Failure Failure Successful [Tested: 21] Successful [Tested: 21]
4.7.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}e^{z} = e^{z}}
\deriv{}{z}e^{z} = e^{z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
diff(exp(z), z) = exp(z)

D[Exp[z], z] == Exp[z]
Successful Successful - Successful [Tested: 7]
4.7.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}e^{az} = ae^{az}}
\deriv{}{z}e^{az} = ae^{az}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
diff(exp(a*z), z) = a*exp(a*z)

D[Exp[a*z], z] == a*Exp[a*z]
Successful Successful - Successful [Tested: 42]
4.7.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}a^{z} = a^{z}\ln@@{a}}
\deriv{}{z}a^{z} = a^{z}\ln@@{a}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a \neq 0} 
diff((a)^(z), z) = (a)^(z)* ln(a)

D[(a)^(z), z] == (a)^(z)* Log[a]
Successful Successful - Successful [Tested: 42]
4.7.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}z^{a} = az^{a-1}}
\deriv{}{z}z^{a} = az^{a-1}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
diff((z)^(a), z) = a*(z)^(a - 1)

D[(z)^(a), z] == a*(z)^(a - 1)
Successful Successful - Successful [Tested: 42]
4.7.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z} = aw}
\deriv[2]{w}{z} = aw		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a \neq 0} 
diff(w, [z$(2)]) = a*w

D[w, {z, 2}] == a*w
Failure Failure
Failed [300 / 300]
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}


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)}


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)}


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}

... skip entries to safe data
Failed [300 / 300]
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]]]}


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]]]}

... skip entries to safe data
4.7.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = Ae^{\sqrt{a}z}+Be^{-\sqrt{a}z}}
w = Ae^{\sqrt{a}z}+Be^{-\sqrt{a}z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w = A*exp(sqrt(a)*z)+ B*exp(-sqrt(a)*z)
 
w == A*Exp[Sqrt[a]*z]+ B*Exp[-Sqrt[a]*z]
 Skipped - no semantic math Skipped - no semantic math - -
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