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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

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{y}{x})

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

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

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

Beliebte Beispiele

tangent f(x)=sqrt(x-8),\at x=9

t an g e n t f (x) = x - 8, at x = 9

integral of 0.06e^{0.04x}

\int 0.06 e^{0.04 x} d x

integral of 3x^2cos(x)

\int 3 x^{2} cos (x) d x

sum from n=0 to infinity of (n!)/(107^n)

n = 0 \sum \infty \frac{n !}{10 7 ^{n}}

derivative of (x^2/(5x+2))

\frac{d}{d x} (\frac{x ^{2}}{5 x + 2})