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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

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

\int \frac{e ^{6 x}}{e ^{6 x} + 7} d x

\int \frac{2 x ^{2}}{20 - 5 x ^{3}} d x

t an g e n t x + \frac{1}{x}

s im pl i f y x^{2} I n (x)

n = 1 \sum \infty \frac{70}{7 ^{n}}