derivative of (f(x(3x))^2-4)

解

\frac{d}{d x} ((f (x) (3 x))^{2} - 4)

9 (2 x^{2} f (x) \frac{d}{d x} (f (x)) + 2 x f (x)^{2})

解答ステップ

\frac{d}{d x} ((f (x) (3 x))^{2} - 4)

簡素化

(f (x) (3 x))^{2} - 4 : 9 x^{2} f (x)^{2} - 4

= \frac{d}{d x} (9 x^{2} f (x)^{2} - 4)

和/差の法則を適用:

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

= \frac{d}{d x} (9 x^{2} f (x)^{2}) - \frac{d}{d x} (4)

\frac{d}{d x} (9 x^{2} f (x)^{2}) = 9 (2 x f (x)^{2} + 2 f (x) \frac{d}{d x} (f (x)) x^{2})

\frac{d}{d x} (4) = 0

= 9 (2 x f (x)^{2} + 2 f (x) \frac{d}{d x} (f (x)) x^{2}) - 0

簡素化

= 9 (2 x^{2} f (x) \frac{d}{d x} (f (x)) + 2 x f (x)^{2})