(\partial)/(\partial x)(sqrt(x^2+4y^2))

Lösung

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

\frac{x}{x ^{2} + 4 y ^{2}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{2 x ^{2} + 4 y ^{2}} \frac{\partial}{\partial x} (x^{2} + 4 y^{2})

= \frac{1}{2 x ^{2} + 4 y ^{2}} \frac{\partial}{\partial x} (x^{2} + 4 y^{2})

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

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

Vereinfache

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

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

x^{2} y^{^{''}} - x y^{^{'}} + y = \frac{1}{x}

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