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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

= - 2 \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

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

Vereinfache

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

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

\frac{d}{d x} (x^{- \frac{4}{3}})

y^{^{'}} + k y = e^{- 7 k x}

d er i v a t i v e \frac{1}{64 + 5 t ^{2}}

\int \frac{1}{x ^{2} + 9} d x

t an g e n t f (x) = 2 x^{3} - x^{2} + 3 x, at x = 1