(\partial)/(\partial u)(sqrt(u^2+v^2))

Lösung

\frac{\partial}{\partial u} (u^{2} + v^{2})

\frac{u}{u ^{2} + v ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial u} (u^{2} + v^{2})

Behandle

v

als Konstante

Wende die Kettenregel an:

\frac{1}{2 u ^{2} + v ^{2}} \frac{\partial}{\partial u} (u^{2} + v^{2})

= \frac{1}{2 u ^{2} + v ^{2}} \frac{\partial}{\partial u} (u^{2} + v^{2})

\frac{\partial}{\partial u} (u^{2} + v^{2}) = 2 u

= \frac{1}{2 u ^{2} + v ^{2}} \cdot 2 u

Vereinfache

\frac{1}{2 u ^{2} + v ^{2}} \cdot 2 u : \frac{u}{u ^{2} + v ^{2}}

= \frac{u}{u ^{2} + v ^{2}}

\int \frac{6 ln ( 4 x )}{5} d x

t an g e n t - 2 sin (x)

d er i v a t i v e f (x) = x^{5} - 3 x + 4

d er i v a t i v e \frac{e ^{x}}{x + 1}

x \to 1 lim (∣ x - 1 ∣)