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Beliebt Rechnen >

derivative-2log_{e}(x)+x^2-4+e^x+x^e

Lösung

ableitung von

- 2 lo g_{e} (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 lo g_{e} (x) + x^{2} - 4 + e^{x} + x^{e})

Vereinfache

- 2 lo g_{e} (x) + x^{2} - 4 + e^{x} + x^{e} : - 2 ln (x) + x^{2} - 4 + e^{x} + x^{e}

= \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

integral of 2csc^4(x)cot^6(x)

\int 2 csc^{4} (x) cot^{6} (x) d x

limit as x approaches-2 of 7-2x

x \to - 2 lim (7 - 2 x)

integral of-2xe^{x^2}

\int - 2 x e^{x^{2}} d x

derivative of 2/(ln(10x^3))

\frac{d}{d x} (\frac{2}{ln ( 10 ) x ^{3}})

integral from 4 to 7 of 1/(sqrt(x^2-16))

\int_{4}^{7} \frac{1}{x ^{2} - 16} d x