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

解

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

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

解答ステップ

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

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))

積の法則を適用:

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

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

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

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