(\partial)/(\partial y)((A^2x^2+B^2y^2)^4)

解

\frac{\partial}{\partial y} ((A^{2} x^{2} + B^{2} y^{2})^{4})

8 B^{2} y (A^{2} x^{2} + B^{2} y^{2})^{3}

解答ステップ

\frac{\partial}{\partial y} ((A^{2} x^{2} + B^{2} y^{2})^{4})

A, B, x

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 y} (A^{2} x^{2} + B^{2} y^{2})

= 4 (A^{2} x^{2} + B^{2} y^{2})^{3} \frac{\partial}{\partial y} (A^{2} x^{2} + B^{2} y^{2})

\frac{\partial}{\partial y} (A^{2} x^{2} + B^{2} y^{2}) = 2 B^{2} y

= 4 (A^{2} x^{2} + B^{2} y^{2})^{3} \cdot 2 B^{2} y

簡素化

= 8 B^{2} y (A^{2} x^{2} + B^{2} y^{2})^{3}