derivative of sin^2(3x+cos(5x^2))

解

\frac{d}{d x} (sin^{2} (3 x) + cos (5 x^{2}))

3 sin (6 x) - sin (5 x^{2}) \cdot 10 x

解答ステップ

\frac{d}{d x} (sin^{2} (3 x) + cos (5 x^{2}))

和/差の法則を適用:

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

= \frac{d}{d x} (sin^{2} (3 x)) + \frac{d}{d x} (cos (5 x^{2}))

\frac{d}{d x} (sin^{2} (3 x)) = 3 sin (6 x)

\frac{d}{d x} (cos (5 x^{2})) = - sin (5 x^{2}) \cdot 10 x

= 3 sin (6 x) - sin (5 x^{2}) \cdot 10 x