derivative of sqrt(1+x-y^2)

解

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

\frac{- 2 y \frac{d y}{d x} + 1}{2 1 + x - y ^{2}}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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