(\partial)/(\partial x)((a^2x^2+b^2y^2)^4)

解

\frac{\partial}{\partial x} ((a^{2} x^{2} + b^{2} y^{2})^{4})

8 a^{2} x (a^{2} x^{2} + b^{2} y^{2})^{3}

解答ステップ

\frac{\partial}{\partial x} ((a^{2} x^{2} + b^{2} y^{2})^{4})

a, b, y

を定数として扱う

連鎖法則を適用:

4 (a^{2} x^{2} + b^{2} y^{2})^{3} \frac{\partial}{\partial x} (a^{2} x^{2} + b^{2} y^{2})

= 4 (a^{2} x^{2} + b^{2} y^{2})^{3} \frac{\partial}{\partial x} (a^{2} x^{2} + b^{2} y^{2})

\frac{\partial}{\partial x} (a^{2} x^{2} + b^{2} y^{2}) = 2 a^{2} x

= 4 (a^{2} x^{2} + b^{2} y^{2})^{3} \cdot 2 a^{2} x

簡素化

= 8 a^{2} x (a^{2} x^{2} + b^{2} y^{2})^{3}