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Popular >

derivative of log_{7}(xe^x)

Solution

derivative of

lo g_{7} (x e^{x})

Solution

\frac{1}{x ln ( 7 )} + lo g_{7} (e)

Solution steps

\frac{d}{d x} (lo g_{7} (x e^{x}))

Simplify

lo g_{7} (x e^{x}) : lo g_{7} (x) + lo g_{7} (e) x

= \frac{d}{d x} (lo g_{7} (x) + lo g_{7} (e) x)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (lo g_{7} (x)) + \frac{d}{d x} (lo g_{7} (e) x)

\frac{d}{d x} (lo g_{7} (x)) = \frac{1}{x ln ( 7 )}

\frac{d}{d x} (lo g_{7} (e) x) = lo g_{7} (e)

= \frac{1}{x ln ( 7 )} + lo g_{7} (e)

Graph

Popular Examples

derivative of (7x/(sqrt(x^2+5)))

\frac{d}{d x} (\frac{7 x}{x ^{2} + 5})

integral of e^xsin(2x)

\int e^{x} sin (2 x) d x

integral of (x(x-2)^2)/(x^4+1)

\int \frac{x ( x - 2 ) ^{2}}{x ^{4} + 1} d x

integral of (cos^2(x))/(cos(x))

\int \frac{cos ^{2} ( x )}{cos ( x )} d x

f^'(x)=(x^2)/(x+1)

f^{^{'}} (x) = \frac{x ^{2}}{x + 1}

Frequently Asked Questions (FAQ)

What is the derivative of log_{7}(xe^x) ?
The derivative of log_{7}(xe^x) is 1/(xln(7))+log_{7}(e)
What is the first derivative of log_{7}(xe^x) ?
The first derivative of log_{7}(xe^x) is 1/(xln(7))+log_{7}(e)