derivative of x^{10}e^{x+10}

解

\frac{d}{d x} (x^{10} e^{x + 10})

10 x^{9} e^{x + 10} + e^{x + 10} x^{10}

解答ステップ

\frac{d}{d x} (x^{10} e^{x + 10})

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{10}, g = e^{x + 10}

= \frac{d}{d x} (x^{10}) e^{x + 10} + \frac{d}{d x} (e^{x + 10}) x^{10}

\frac{d}{d x} (x^{10}) = 10 x^{9}

\frac{d}{d x} (e^{x + 10}) = e^{x + 10}

= 10 x^{9} e^{x + 10} + e^{x + 10} x^{10}