derivative of {f}(x(x)^{-1}(x^2))

解

\frac{d}{d x} (f (x) (x)^{- 1} (x^{2}))

f (x) + x \frac{d}{d x} (f (x))

解答ステップ

\frac{d}{d x} (f (x) (x)^{- 1} (x^{2}))

簡素化

f (x) (x)^{- 1} (x^{2}) : x f (x)

= \frac{d}{d x} (x f (x))

積の法則を適用:

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

f = x, g = f (x)

= \frac{d x}{d x} f (x) + \frac{d}{d x} (f (x)) x

\frac{d x}{d x} = 1

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

簡素化

= f (x) + x \frac{d}{d x} (f (x))