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

Lösung

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

y + \frac{1}{x}

Schritte zur Lösung

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

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

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

= y + \frac{1}{x}

\int \frac{- 16 x + 3}{( x ^{2} + 2 ) ^{2}} d x

\frac{\partial}{\partial x} (e^{(3 x + 4 y)} cos (5 z))

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\frac{d}{d x} (\frac{x ^{2} - 9 x + 20}{( x - 2 ) ( x + 2 )})

\int sinh (6 x) d x