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

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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