derivative of 10x^{10}e^x

解

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

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

解答ステップ

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

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

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

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

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

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