What is the derivative of ln(xe^{-6x}) ?

The derivative of ln(xe^{-6x}) is 1/x-6

What is the first derivative of ln(xe^{-6x}) ?

The first derivative of ln(xe^{-6x}) is 1/x-6

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derivative of

ln (x e^{- 6 x})

\frac{1}{x} - 6

Solution steps

\frac{d}{d x} (ln (x e^{- 6 x}))

Simplify

ln (x e^{- 6 x}) : ln (x) - 6 x

= \frac{d}{d x} (ln (x) - 6 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (ln (x)) - \frac{d}{d x} (6 x)

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

\frac{d}{d x} (6 x) = 6

= \frac{1}{x} - 6

What is the derivative of ln(xe^{-6x}) ?
The derivative of ln(xe^{-6x}) is 1/x-6
What is the first derivative of ln(xe^{-6x}) ?
The first derivative of ln(xe^{-6x}) is 1/x-6