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Beliebt Rechnen >

(\partial)/(\partial y)(1/2 ln(x^2+y^2))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Beliebte Beispiele

(\partial)/(\partial x)(e^{2x})

\frac{\partial}{\partial x} (e^{2 x})

integral of (x^2+1)^5*x

\int (x^{2} + 1)^{5} \cdot x d x

(d^3)/(dx^3)(ln(x))

\frac{d ^{3}}{d x ^{3}} (ln (x))

derivative of 6/x-2/(x^3+1/(x^4))

\frac{d}{d x} (\frac{6}{x} - \frac{2}{x ^{3}} + \frac{1}{x ^{4}})

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d er i v a t i v e y = x^{- 8 c o s (x)}