(\partial)/(\partial x)(cos^3(x^7y^7))

解

\frac{\partial}{\partial x} (cos^{3} (x^{7} y^{7}))

- 21 x^{6} y^{7} cos^{2} (x^{7} y^{7}) sin (x^{7} y^{7})

解答ステップ

\frac{\partial}{\partial x} (cos^{3} (x^{7} y^{7}))

y

を定数として扱う

連鎖法則を適用:

3 (cos (x^{7} y^{7}))^{2} \frac{\partial}{\partial x} (cos (x^{7} y^{7}))

= 3 (cos (x^{7} y^{7}))^{2} \frac{\partial}{\partial x} (cos (x^{7} y^{7}))

\frac{\partial}{\partial x} (cos (x^{7} y^{7})) = - sin (x^{7} y^{7}) \cdot 7 y^{7} x^{6}

= 3 (cos (x^{7} y^{7}))^{2} (- sin (x^{7} y^{7}) \cdot 7 y^{7} x^{6})

簡素化

= - 21 x^{6} y^{7} cos^{2} (x^{7} y^{7}) sin (x^{7} y^{7})