(\partial)/(\partial x)((x^2-y^2)^{0.5})

解

\frac{\partial}{\partial x} ((x^{2} - y^{2})^{0.5})

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

解答ステップ

\frac{\partial}{\partial x} ((x^{2} - y^{2})^{0.5})

y

を定数として扱う

連鎖法則を適用:

\frac{0.5}{( x ^{2} - y ^{2} ) ^{0.5}} \frac{\partial}{\partial x} (x^{2} - y^{2})

= \frac{0.5}{( x ^{2} - y ^{2} ) ^{0.5}} \frac{\partial}{\partial x} (x^{2} - y^{2})

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

= \frac{0.5}{( x ^{2} - y ^{2} ) ^{0.5}} \cdot 2 x

簡素化

\frac{0.5}{( x ^{2} - y ^{2} ) ^{\frac{1}{2}}} \cdot 2 x : \frac{x}{( x ^{2} - y ^{2} ) ^{\frac{1}{2}}}

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