What is the derivative of ln(xe^{-8x}) ?

The derivative of ln(xe^{-8x}) is 1/x-8

What is the first derivative of ln(xe^{-8x}) ?

The first derivative of ln(xe^{-8x}) is 1/x-8

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derivative of

ln (x e^{- 8 x})

\frac{1}{x} - 8

Solution steps

\frac{d}{d x} (ln (x e^{- 8 x}))

Simplify

ln (x e^{- 8 x}) : ln (x) - 8 x

= \frac{d}{d x} (ln (x) - 8 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (ln (x)) - \frac{d}{d x} (8 x)

\frac{d}{d x} (ln (x)) = \frac{1}{x}

\frac{d}{d x} (8 x) = 8

= \frac{1}{x} - 8

\frac{d}{d x} (\frac{4 x}{4 + x})

\int (7 x + 6)^{4} d x

t \to 0 lim (\frac{6}{t} - \frac{6}{t ^{2} + t})

\int \frac{x ^{3}}{25 - x ^{2}} d x

\frac{d}{d x} (x^{2} + 45)

What is the derivative of ln(xe^{-8x}) ?
The derivative of ln(xe^{-8x}) is 1/x-8
What is the first derivative of ln(xe^{-8x}) ?
The first derivative of ln(xe^{-8x}) is 1/x-8