(\partial)/(\partial y)(tan(x^3y^2))

解

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

sec^{2} (x^{3} y^{2}) \cdot 2 x^{3} y

解答ステップ

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

x

を定数として扱う

連鎖法則を適用:

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

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

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

= sec^{2} (x^{3} y^{2}) \cdot 2 x^{3} y