(\partial)/(\partial x)(cos^6(x^9y^3))

解

\frac{\partial}{\partial x} (cos^{6} (x^{9} y^{3}))

- 54 x^{8} y^{3} cos^{5} (x^{9} y^{3}) sin (x^{9} y^{3})

解答ステップ

\frac{\partial}{\partial x} (cos^{6} (x^{9} y^{3}))

y

を定数として扱う

連鎖法則を適用:

6 (cos (x^{9} y^{3}))^{5} \frac{\partial}{\partial x} (cos (x^{9} y^{3}))

= 6 (cos (x^{9} y^{3}))^{5} \frac{\partial}{\partial x} (cos (x^{9} y^{3}))

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

= 6 (cos (x^{9} y^{3}))^{5} (- sin (x^{9} y^{3}) \cdot 9 y^{3} x^{8})

簡素化

= - 54 x^{8} y^{3} cos^{5} (x^{9} y^{3}) sin (x^{9} y^{3})