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

Lösung

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

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

Schritte zur Lösung

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

Behandle

z, x

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial y} (z) = 0

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

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

Vereinfache

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

d er i v a t i v e - 3 e^{x^{5}}

\int \frac{( x - 1 )}{( x + 1 )} d x

\int \frac{2}{25 - 2 x ^{2}} d x

d er i v a t i v e 6 x + \frac{4}{x}

n = 1 \sum \infty \frac{1}{n ( ln ( n ) )}