derivative of cos^{7/4}(4x^3)

解

\frac{d}{d x} (cos^{\frac{7}{4}} (4 x^{3}))

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

解答ステップ

\frac{d}{d x} (cos^{\frac{7}{4}} (4 x^{3}))

連鎖法則を適用:

\frac{7 ( cos ( 4 x ^{3} ) ) ^{\frac{3}{4}}}{4} \frac{d}{d x} (cos (4 x^{3}))

= \frac{7 ( cos ( 4 x ^{3} ) ) ^{\frac{3}{4}}}{4} \frac{d}{d x} (cos (4 x^{3}))

\frac{d}{d x} (cos (4 x^{3})) = - sin (4 x^{3}) \cdot 12 x^{2}

= \frac{7 ( cos ( 4 x ^{3} ) ) ^{\frac{3}{4}}}{4} (- sin (4 x^{3}) \cdot 12 x^{2})

簡素化

\frac{7 cos ^{\frac{3}{4}} ( 4 x ^{3} )}{4} (- sin (4 x^{3}) \cdot 12 x^{2}) : - 21 x^{2} sin (4 x^{3}) cos^{\frac{3}{4}} (4 x^{3})

= - 21 x^{2} sin (4 x^{3}) cos^{\frac{3}{4}} (4 x^{3})