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

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (1) = 0

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

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

Vereinfache

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

\int \frac{x + 1}{3 x + 2} d x

\int_{- 3}^{1} x d x

x \to \infty lim (2 ln (x))

x \to - 6 lim (5 x^{2} + 6 x + a)

\int_{0}^{e} \frac{1}{x + e} d x