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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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