(\partial)/(\partial x)(sin(5x^4y-3xy^4))

解

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

cos (5 x^{4} y - 3 x y^{4}) (20 y x^{3} - 3 y^{4})

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

\frac{\partial}{\partial x} (5 x^{4} y - 3 x y^{4}) = 20 y x^{3} - 3 y^{4}

= cos (5 x^{4} y - 3 x y^{4}) (20 y x^{3} - 3 y^{4})