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Popular >

derivative of log_{5}(xe^x)

Solution

\frac{d}{d x} (lo g_{5} (x e^{x}))

Solution

\frac{1}{x ln ( 5 )} + lo g_{5} (e)

Solution steps

\frac{d}{d x} (lo g_{5} (x e^{x}))

Simplify

lo g_{5} (x e^{x}) : lo g_{5} (x) + lo g_{5} (e) x

= \frac{d}{d x} (lo g_{5} (x) + lo g_{5} (e) x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (lo g_{5} (x)) + \frac{d}{d x} (lo g_{5} (e) x)

\frac{d}{d x} (lo g_{5} (x)) = \frac{1}{x ln ( 5 )}

\frac{d}{d x} (lo g_{5} (e) x) = lo g_{5} (e)

= \frac{1}{x ln ( 5 )} + lo g_{5} (e)

Popular Examples

integral of (tan^2(x))/4

\int \frac{tan ^{2} ( x )}{4} d x

derivative of x^{3x}derivative of

x^{3 x}

derivative of (8x/(5-tan(x)))

\frac{d}{d x} (\frac{8 x}{5 - tan ( x )})

y^'-6/x y=x^{-4}y^5,y(1)=1

y^{^{'}} - \frac{6}{x} y = x^{- 4} y^{5}, y (1) = 1

integral from 0 to infinity of 4e^{-4x}

\int_{0}^{\infty} 4 e^{- 4 x} d x

Frequently Asked Questions (FAQ)

What is the derivative of log_{5}(xe^x) ?
The derivative of log_{5}(xe^x) is 1/(xln(5))+log_{5}(e)
What is the first derivative of log_{5}(xe^x) ?
The first derivative of log_{5}(xe^x) is 1/(xln(5))+log_{5}(e)