derivative of 2e^x-3x^e+sqrt(e)

Lösung

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

- 3 e x^{e - 1} + 2 e^{x}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (2 e^{x}) - \frac{d}{d x} (3 x^{e}) + \frac{d}{d x} (e)

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

\frac{d}{d x} (3 x^{e}) = 3 e x^{e - 1}

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

= 2 e^{x} - 3 e x^{e - 1} + 0

Vereinfache

= - 3 e x^{e - 1} + 2 e^{x}

x \to 0 lim (\frac{2 + sin ( x )}{x})

\int 2 x + 5 d x

x \to 6 lim (x - 5)

\int (x + 1) d x

x \to - 2 lim (\frac{x + 1}{x ^{3} + 8})