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Beliebt Rechnen >

derivative of x^y-y^x

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Beliebte Beispiele

y^{^{'}} - y = x^{2}

limit as x approaches 7 of sqrt(3x-5)

x \to 7 lim (3 x - 5)

limit as x approaches 0 of (2x^2+5x+7)/x

x \to 0 lim (\frac{2 x ^{2} + 5 x + 7}{x})

derivative of cos(sin(5x))

\frac{d}{d x} (cos (sin (5 x)))

xy^'+y=40sqrt(x)

x y^{^{'}} + y = 40 x