derivative of f(h,x(g(h,x)(h(x))))

解

\frac{d}{d x} (f (h, x) (g (h, x) (h (x))))

h (\frac{d}{d x} (f (h, x)) g (h, x) x + (\frac{d}{d x} (g (h, x)) x + 1 \cdot g (h, x)) f (h, x))

解答ステップ

\frac{d}{d x} (f (h, x) (g (h, x) (h (x))))

h

を定数として扱う

定数を除去:

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

= h \frac{d}{d x} (f (h, x) g (h, x) x)

積の法則を適用:

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

f = f (h, x), g = g (h, x) x

= h (\frac{d}{d x} (f (h, x)) g (h, x) x + \frac{d}{d x} (g (h, x) x) f (h, x))

\frac{d}{d x} (g (h, x) x) = \frac{d}{d x} (g (h, x)) x + 1 \cdot g (h, x)

= h (\frac{d}{d x} (f (h, x)) g (h, x) x + (\frac{d}{d x} (g (h, x)) x + 1 \cdot g (h, x)) f (h, x))