What is the derivative of ln(x^2e^{-x}) ?

The derivative of ln(x^2e^{-x}) is 2/x-1

What is the first derivative of ln(x^2e^{-x}) ?

The first derivative of ln(x^2e^{-x}) is 2/x-1

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\frac{d}{d x} (ln (x^{2} e^{- x}))

\frac{2}{x} - 1

Solution steps

\frac{d}{d x} (ln (x^{2} e^{- x}))

Simplify

ln (x^{2} e^{- x}) : ln (x^{2}) - x

= \frac{d}{d x} (ln (x^{2}) - x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (ln (x^{2})) - \frac{d x}{d x}

\frac{d}{d x} (ln (x^{2})) = \frac{2}{x}

\frac{d x}{d x} = 1

= \frac{2}{x} - 1

x y - 2 y^{2} = 5, (11, 5)

\int_{1}^{2} \frac{9}{x ^{3} + 4 x} d x

\frac{d}{d x} (\frac{5}{2} x^{2})

y = - \frac{6}{x}, at x = - 4

\frac{d}{d x} (cot^{2} (3 x))

What is the derivative of ln(x^2e^{-x}) ?
The derivative of ln(x^2e^{-x}) is 2/x-1
What is the first derivative of ln(x^2e^{-x}) ?
The first derivative of ln(x^2e^{-x}) is 2/x-1