(\partial)/(\partial y)(tan(2+2x^2y^4z^2))

解

\frac{\partial}{\partial y} (tan (2 + 2 x^{2} y^{4} z^{2}))

sec^{2} (2 + 2 x^{2} y^{4} z^{2}) \cdot 8 x^{2} z^{2} y^{3}

解答ステップ

\frac{\partial}{\partial y} (tan (2 + 2 x^{2} y^{4} z^{2}))

x, z

を定数として扱う

連鎖法則を適用:

sec^{2} (2 + 2 x^{2} y^{4} z^{2}) \frac{\partial}{\partial y} (2 + 2 x^{2} y^{4} z^{2})

= sec^{2} (2 + 2 x^{2} y^{4} z^{2}) \frac{\partial}{\partial y} (2 + 2 x^{2} y^{4} z^{2})

\frac{\partial}{\partial y} (2 + 2 x^{2} y^{4} z^{2}) = 8 x^{2} z^{2} y^{3}

= sec^{2} (2 + 2 x^{2} y^{4} z^{2}) \cdot 8 x^{2} z^{2} y^{3}