derivative of f(x(5x^2-4))

解

\frac{d}{d x} (f (x) (5 x^{2} - 4))

\frac{d}{d x} (f (x)) (5 x^{2} - 4) + 10 x f (x)

解答ステップ

\frac{d}{d x} (f (x) (5 x^{2} - 4))

積の法則を適用:

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

f = f (x), g = 5 x^{2} - 4

= \frac{d}{d x} (f (x)) (5 x^{2} - 4) + \frac{d}{d x} (5 x^{2} - 4) f (x)

\frac{d}{d x} (5 x^{2} - 4) = 10 x

= \frac{d}{d x} (f (x)) (5 x^{2} - 4) + 10 x f (x)