derivative of {g}(x(x)^2(x))

解

\frac{d}{d x} (g (x) (x)^{2} (x))

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

解答ステップ

\frac{d}{d x} (g (x) (x)^{2} (x))

簡素化

g (x) (x)^{2} (x) : x^{3} g (x)

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

積の法則を適用:

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

f = x^{3}, g = g (x)

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

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

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