derivative of-sqrt(x^2+y^2)-10

解

\frac{d}{d x} (- x^{2} + y^{2} - 10)

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

解答ステップ

\frac{d}{d x} (- x^{2} + y^{2} - 10)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d x} (x^{2} + y^{2}) - \frac{d}{d x} (10)

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

\frac{d}{d x} (10) = 0

= - \frac{x + y \frac{d y}{d x}}{x ^{2} + y ^{2}} - 0

簡素化

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