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Beliebt Rechnen >

derivative of e^{xy}+ln(x/y)

Lösung

\frac{d}{d x} (e^{x y} + ln (\frac{x}{y}))

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (e^{x y} + ln (\frac{x}{y}))

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (ln (\frac{x}{y})) = \frac{y - x \frac{d y}{d x}}{x y}

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

Beliebte Beispiele

(dy)/(dx)=4+sqrt(y-4x+2)

\frac{d y}{d x} = 4 + y - 4 x + 2

limit as x approaches 0 of ax

x \to 0 lim (a x)

derivative of 2x^{2x}

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

(\partial)/(\partial x)(x-y^4)

\frac{\partial}{\partial x} (x - y^{4})

limit as x approaches 0 of (tan(a)x)/x

x \to 0 lim (\frac{tan ( a ) x}{x})