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Beliebt Rechnen >

derivative f(x)=-2ln(x)+x^2-4+e^x+x^e

Lösung

ableitung von

f (x) = - 2 ln (x) + x^{2} - 4 + e^{x} + x^{e}

Lösung

2 x + e x^{e - 1} + e^{x} - \frac{2}{x}

Schritte zur Lösung

\frac{d}{d x} (- 2 ln (x) + x^{2} - 4 + e^{x} + x^{e})

Wende die Summen-/Differenzregel an:

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

= - \frac{d}{d x} (2 ln (x)) + \frac{d}{d x} (x^{2}) - \frac{d}{d x} (4) + \frac{d}{d x} (e^{x}) + \frac{d}{d x} (x^{e})

\frac{d}{d x} (2 ln (x)) = \frac{2}{x}

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

\frac{d}{d x} (4) = 0

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

\frac{d}{d x} (x^{e}) = e x^{e - 1}

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

Vereinfache

= 2 x + e x^{e - 1} + e^{x} - \frac{2}{x}

Graph

Beliebte Beispiele

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