derivative of \sqrt[3]{sin^2(2x})

解

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

\frac{2 sin ( 4 x )}{3 sin ^{\frac{4}{3}} ( 2 x )}

解答ステップ

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

連鎖法則を適用:

\frac{1}{3 ( sin ^{2} ( 2 x ) ) ^{\frac{2}{3}}} \frac{d}{d x} (sin^{2} (2 x))

= \frac{1}{3 ( sin ^{2} ( 2 x ) ) ^{\frac{2}{3}}} \frac{d}{d x} (sin^{2} (2 x))

\frac{d}{d x} (sin^{2} (2 x)) = 2 sin (4 x)

= \frac{1}{3 ( sin ^{2} ( 2 x ) ) ^{\frac{2}{3}}} \cdot 2 sin (4 x)

簡素化

\frac{1}{3 ( sin ^{2} ( 2 x ) ) ^{\frac{2}{3}}} \cdot 2 sin (4 x) : \frac{2 sin ( 4 x )}{3 sin ^{\frac{4}{3}} ( 2 x )}

= \frac{2 sin ( 4 x )}{3 sin ^{\frac{4}{3}} ( 2 x )}