(\partial)/(\partial x)(tan(5+2x^2y^3z^2))

解

\frac{\partial}{\partial x} (tan (5 + 2 x^{2} y^{3} z^{2}))

sec^{2} (5 + 2 x^{2} y^{3} z^{2}) \cdot 4 y^{3} z^{2} x

解答ステップ

\frac{\partial}{\partial x} (tan (5 + 2 x^{2} y^{3} z^{2}))

y, z

を定数として扱う

連鎖法則を適用:

sec^{2} (5 + 2 x^{2} y^{3} z^{2}) \frac{\partial}{\partial x} (5 + 2 x^{2} y^{3} z^{2})

= sec^{2} (5 + 2 x^{2} y^{3} z^{2}) \frac{\partial}{\partial x} (5 + 2 x^{2} y^{3} z^{2})

\frac{\partial}{\partial x} (5 + 2 x^{2} y^{3} z^{2}) = 4 y^{3} z^{2} x

= sec^{2} (5 + 2 x^{2} y^{3} z^{2}) \cdot 4 y^{3} z^{2} x