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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

k, y

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Beliebte Beispiele

sum from n=1 to infinity of (-1/2)^{n+1}

n = 1 \sum \infty (- \frac{1}{2})^{n + 1}

integral of cos^5(x)tan^4(x)

\int cos^{5} (x) tan^{4} (x) d x

(dy)/(dx)(1+e^x)=e^{x-y}

\frac{d y}{d x} (1 + e^{x}) = e^{x - y}

tangent f(x)=e^x,\at x=ln(2)

t an g e n t f (x) = e^{x}, at x = ln (2)

(\partial)/(\partial x)(2x-ye^y)

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