(\partial)/(\partial x)((4x-y^2)^{3/2})

解

\frac{\partial}{\partial x} ((4 x - y^{2})^{\frac{3}{2}})

6 (4 x - y^{2})^{\frac{1}{2}}

解答ステップ

\frac{\partial}{\partial x} ((4 x - y^{2})^{\frac{3}{2}})

y

を定数として扱う

連鎖法則を適用:

\frac{3 ( 4 x - y ^{2} ) ^{\frac{1}{2}}}{2} \frac{\partial}{\partial x} (4 x - y^{2})

= \frac{3 ( 4 x - y ^{2} ) ^{\frac{1}{2}}}{2} \frac{\partial}{\partial x} (4 x - y^{2})

\frac{\partial}{\partial x} (4 x - y^{2}) = 4

= \frac{3 ( 4 x - y ^{2} ) ^{\frac{1}{2}}}{2} \cdot 4

簡素化

\frac{3 ( 4 x - y ^{2} ) ^{\frac{1}{2}}}{2} \cdot 4 : 6 (4 x - y^{2})^{\frac{1}{2}}

= 6 (4 x - y^{2})^{\frac{1}{2}}