derivative of c+x+{f}(x(x)^2)

解

\frac{d}{d x} (c + x + f (x) (x)^{2})

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

解答ステップ

\frac{d}{d x} (c + x + f (x) (x)^{2})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d c}{d x} + \frac{d x}{d x} + \frac{d}{d x} (f (x) x^{2})

\frac{d c}{d x} = 0

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

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

= 0 + 1 + \frac{d}{d x} (f (x)) x^{2} + 2 x f (x)

簡素化

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