(\partial)/(\partial x)(cos^4(x^3y^5))

解

\frac{\partial}{\partial x} (cos^{4} (x^{3} y^{5}))

- 12 x^{2} y^{5} cos^{3} (x^{3} y^{5}) sin (x^{3} y^{5})

解答ステップ

\frac{\partial}{\partial x} (cos^{4} (x^{3} y^{5}))

y

を定数として扱う

連鎖法則を適用:

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

= 4 (cos (x^{3} y^{5}))^{3} \frac{\partial}{\partial x} (cos (x^{3} y^{5}))

\frac{\partial}{\partial x} (cos (x^{3} y^{5})) = - sin (x^{3} y^{5}) \cdot 3 y^{5} x^{2}

= 4 (cos (x^{3} y^{5}))^{3} (- sin (x^{3} y^{5}) \cdot 3 y^{5} x^{2})

簡素化

= - 12 x^{2} y^{5} cos^{3} (x^{3} y^{5}) sin (x^{3} y^{5})