(\partial)/(\partial x)(cos^6(x^2y^9))

解

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

- 12 x y^{9} cos^{5} (x^{2} y^{9}) sin (x^{2} y^{9})

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

6 (cos (x^{2} y^{9}))^{5} \frac{\partial}{\partial x} (cos (x^{2} y^{9}))

= 6 (cos (x^{2} y^{9}))^{5} \frac{\partial}{\partial x} (cos (x^{2} y^{9}))

\frac{\partial}{\partial x} (cos (x^{2} y^{9})) = - sin (x^{2} y^{9}) \cdot 2 y^{9} x

= 6 (cos (x^{2} y^{9}))^{5} (- sin (x^{2} y^{9}) \cdot 2 y^{9} x)

簡素化

= - 12 x y^{9} cos^{5} (x^{2} y^{9}) sin (x^{2} y^{9})