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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

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

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

\frac{\partial}{\partial x} (\frac{1}{y}) = 0

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

Vereinfache

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

Beliebte Beispiele

tangent f(x)=sqrt(9-6x),\at x=-1

t an g e n t f (x) = 9 - 6 x, at x = - 1

inverselaplace-3/(s+3)+4/(s-4)

in v erse l a pl a ce - \frac{3}{s + 3} + \frac{4}{s - 4}

integral of 8/(x^{-1)+2}

\int \frac{8}{x ^{- 1} + 2} d x

steigung y=4x^2-x

s l o p e y = 4 x^{2} - x

derivative (e^x+1)/(e^{2x)}

d er i v a t i v e \frac{e ^{x} + 1}{e ^{2 x}}