derivative of cos^9(x^2y^6)

解

\frac{d}{d x} (cos^{9} (x^{2} y^{6}))

- 9 cos^{8} (x^{2} y^{6}) sin (x^{2} y^{6}) (2 x y^{6} + 6 x^{2} y^{5} \frac{d y}{d x})

解答ステップ

\frac{d}{d x} (cos^{9} (x^{2} y^{6}))

連鎖法則を適用:

9 (cos (x^{2} y^{6}))^{8} \frac{d}{d x} (cos (x^{2} y^{6}))

= 9 (cos (x^{2} y^{6}))^{8} \frac{d}{d x} (cos (x^{2} y^{6}))

\frac{d}{d x} (cos (x^{2} y^{6})) = - sin (x^{2} y^{6}) (2 x y^{6} + 6 y^{5} \frac{d y}{d x} x^{2})

= 9 (cos (x^{2} y^{6}))^{8} (- sin (x^{2} y^{6}) (2 x y^{6} + 6 y^{5} \frac{d y}{d x} x^{2}))

簡素化

= - 9 cos^{8} (x^{2} y^{6}) sin (x^{2} y^{6}) (2 x y^{6} + 6 x^{2} y^{5} \frac{d y}{d x})