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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

y^{^{'}} t^{4} = 0

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