4.7

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
4.7.E1	${\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}\ln z=\frac{1}{z}}}$ \deriv{}{z}\ln@@{z} = \frac{1}{z}		diff(ln(z), z) = (1)/(z)	D[Log[z], z] == Divide[1,z]	Successful	Successful	-	Successful [Tested: 7]
4.7.E2	${\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{Ln}z=\frac{1}{z}}}$ \deriv{}{z}\Ln@@{z} = \frac{1}{z}		diff(ln(z), z) = (1)/(z)	D[Log[z], z] == Divide[1,z]	Successful	Successful	-	Successful [Tested: 7]
4.7.E3	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\ln z=(-1)^{n-1}(n-1)!z^{-n}}}$ \deriv[n]{}{z}\ln@@{z} = (-1)^{n-1}(n-1)!z^{-n}		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	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\operatorname{Ln}z=(-1)^{n-1}(n-1)!z^{-n}}}$ \deriv[n]{}{z}\Ln@@{z} = (-1)^{n-1}(n-1)!z^{-n}		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	${\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}e^{z}=e^{z}}}$ \deriv{}{z}e^{z} = e^{z}		diff(exp(z), z) = exp(z)	D[Exp[z], z] == Exp[z]	Successful	Successful	-	Successful [Tested: 7]
4.7.E8	${\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}e^{az}=ae^{az}}}$ \deriv{}{z}e^{az} = ae^{az}		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	${\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}a^{z}=a^{z}\ln a}}$ \deriv{}{z}a^{z} = a^{z}\ln@@{a}	${\displaystyle{\displaystyle a\neq 0}}$	diff((a)^(z), z) = (a)^(z)* ln(a)	D[(a)^(z), z] == (a)^(z)* Log[a]	Successful	Successful	-	Successful [Tested: 42]
4.7.E10	${\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}z^{a}=az^{a-1}}}$ \deriv{}{z}z^{a} = az^{a-1}		diff((z)^(a), z) = a*(z)^(a - 1)	D[(z)^(a), z] == a*(z)^(a - 1)	Successful	Successful	-	Successful [Tested: 42]
4.7.E14	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}=aw}}$ \deriv[2]{w}{z} = aw	${\displaystyle{\displaystyle a\neq 0}}$	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	${\displaystyle{\displaystyle w=Ae^{\sqrt{a}z}+Be^{-\sqrt{a}z}}}$ w = Ae^{\sqrt{a}z}+Be^{-\sqrt{a}z}		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	-	-