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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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