derivative of sqrt({r)(x(x)^2-x^2})

解

\frac{d}{d x} (r (x) (x)^{2} - x^{2})

\frac{x \frac{d}{d x} ( r ( x ) ) + 2 r ( x ) - 2}{2 r ( x ) - 1}

解答ステップ

\frac{d}{d x} (r (x) (x)^{2} - x^{2})

連鎖法則を適用:

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

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

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

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

簡素化

\frac{1}{2 r ( x ) x ^{2} - x ^{2}} (\frac{d}{d x} (r (x)) x^{2} + 2 x r (x) - 2 x) : \frac{x \frac{d}{d x} ( r ( x ) ) + 2 r ( x ) - 2}{2 r ( x ) - 1}

= \frac{x \frac{d}{d x} ( r ( x ) ) + 2 r ( x ) - 2}{2 r ( x ) - 1}