derivative (x^2-y^2)^{1/2}

解

導関数

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

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

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

\frac{1}{2 ( 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}}}