What is the derivative of g(x)=ln(xe^{-7x}) ?

The derivative of g(x)=ln(xe^{-7x}) is 1/x-7

What is the first derivative of g(x)=ln(xe^{-7x}) ?

The first derivative of g(x)=ln(xe^{-7x}) is 1/x-7

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derivative of

g (x) = ln (x e^{- 7 x})

\frac{1}{x} - 7

Solution steps

\frac{d}{d x} (ln (x e^{- 7 x}))

Simplify

ln (x e^{- 7 x}) : ln (x) - 7 x

= \frac{d}{d x} (ln (x) - 7 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (ln (x)) - \frac{d}{d x} (7 x)

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

\frac{d}{d x} (7 x) = 7

= \frac{1}{x} - 7

What is the derivative of g(x)=ln(xe^{-7x}) ?
The derivative of g(x)=ln(xe^{-7x}) is 1/x-7
What is the first derivative of g(x)=ln(xe^{-7x}) ?
The first derivative of g(x)=ln(xe^{-7x}) is 1/x-7