What is the derivative of ln(xe^{-3x}) ?

The derivative of ln(xe^{-3x}) is 1/x-3

What is the first derivative of ln(xe^{-3x}) ?

The first derivative of ln(xe^{-3x}) is 1/x-3

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derivative of

ln (x e^{- 3 x})

\frac{1}{x} - 3

Solution steps

\frac{d}{d x} (ln (x e^{- 3 x}))

Simplify

ln (x e^{- 3 x}) : ln (x) - 3 x

= \frac{d}{d x} (ln (x) - 3 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (ln (x)) - \frac{d}{d x} (3 x)

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

\frac{d}{d x} (3 x) = 3

= \frac{1}{x} - 3

f (x) = \frac{9}{x}

\int e^{- x^{2} \frac{1}{2}} d x

\frac{d}{d x} (\frac{2 x + 6 x ^{2}}{( 1 + 6 x ) ^{2}})

y + x^{2} + y^{2} d x - x d y = 0

y^{^{''}} - 3 y^{^{'}} - 4 y = 0, y (0) = a, y^{^{'}} (0) = - 20

What is the derivative of ln(xe^{-3x}) ?
The derivative of ln(xe^{-3x}) is 1/x-3
What is the first derivative of ln(xe^{-3x}) ?
The first derivative of ln(xe^{-3x}) is 1/x-3