derivative of e^{{g}(x(x^3)-2})

解

\frac{d}{d x} (e^{g (x) (x^{3}) - 2})

e^{g (x) x^{3} - 2} (x^{3} \frac{d}{d x} (g (x)) + 3 x^{2} g (x))

解答ステップ

\frac{d}{d x} (e^{g (x) (x^{3}) - 2})

連鎖法則を適用:

e^{g (x) x^{3} - 2} \frac{d}{d x} (g (x) x^{3} - 2)

= e^{g (x) x^{3} - 2} \frac{d}{d x} (g (x) x^{3} - 2)

\frac{d}{d x} (g (x) x^{3} - 2) = x^{3} \frac{d}{d x} (g (x)) + 3 x^{2} g (x)

= e^{g (x) x^{3} - 2} (x^{3} \frac{d}{d x} (g (x)) + 3 x^{2} g (x))