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Beliebt Rechnen >

(\partial)/(\partial x)(xy+1/x+8/y)

Lösung

\frac{\partial}{\partial x} (x y + \frac{1}{x} + \frac{8}{y})

Lösung

y - \frac{1}{x ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (x y + \frac{1}{x} + \frac{8}{y})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x y) + \frac{\partial}{\partial x} (\frac{1}{x}) + \frac{\partial}{\partial x} (\frac{8}{y})

\frac{\partial}{\partial x} (x y) = y

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

\frac{\partial}{\partial x} (\frac{8}{y}) = 0

= y - \frac{1}{x ^{2}} + 0

Vereinfache

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

Beliebte Beispiele

sum from n=1 to infinity of 1/((3+2n)^2)

n = 1 \sum \infty \frac{1}{( 3 + 2 n ) ^{2}}

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\int_{1}^{\infty} 21 \frac{e - x}{x} d x

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t^2y^{''}-2ty^'-4y=0

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