(\partial)/(\partial x)(-sqrt(x^2+y^2))

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

- \frac{1}{2 x ^{2} + y ^{2}} \cdot 2 x : - \frac{x}{x ^{2} + y ^{2}}

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

t^{2} y^{^{''}} - 2 y = 3 t^{2} - 1

x \to 0 lim (\frac{( 1 )}{x})

y^{^{'}} = (1 - y) (2 - y)

(ln (e))^{^{'}}

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