(\partial)/(\partial x)(cos^9(x^4y^8))

解

\frac{\partial}{\partial x} (cos^{9} (x^{4} y^{8}))

- 36 x^{3} y^{8} cos^{8} (x^{4} y^{8}) sin (x^{4} y^{8})

解答ステップ

\frac{\partial}{\partial x} (cos^{9} (x^{4} y^{8}))

y

を定数として扱う

連鎖法則を適用:

9 (cos (x^{4} y^{8}))^{8} \frac{\partial}{\partial x} (cos (x^{4} y^{8}))

= 9 (cos (x^{4} y^{8}))^{8} \frac{\partial}{\partial x} (cos (x^{4} y^{8}))

\frac{\partial}{\partial x} (cos (x^{4} y^{8})) = - sin (x^{4} y^{8}) \cdot 4 y^{8} x^{3}

= 9 (cos (x^{4} y^{8}))^{8} (- sin (x^{4} y^{8}) \cdot 4 y^{8} x^{3})

簡素化

= - 36 x^{3} y^{8} cos^{8} (x^{4} y^{8}) sin (x^{4} y^{8})