derivative of \sqrt[4]{sin(x^3})

解

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

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

解答ステップ

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

連鎖法則を適用:

\frac{1}{4 ( sin ( x ^{3} ) ) ^{\frac{3}{4}}} \frac{d}{d x} (sin (x^{3}))

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

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

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

簡素化

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

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