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

解

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

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

解答ステップ

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

和/差の法則を適用:

(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}