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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial y} (x^{2} + 2 y^{2}) = 4 y

= \frac{1}{2 x ^{2} + 2 y ^{2}} \cdot 4 y

Vereinfache

\frac{1}{2 x ^{2} + 2 y ^{2}} \cdot 4 y : \frac{2 y}{x ^{2} + 2 y ^{2}}

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

\frac{d y}{d x} = 4 x - y

\int \frac{x ^{2} - 3 x + 1}{x + 1} d x

\frac{\partial}{\partial y} (3 x e^{- 2 x y})

\int \frac{1}{x ^{2} + 4 x + 8} d x

5 e^{2 x} \frac{d y}{d x} = - 10 \frac{x}{y ^{2}}