derivative f(x)=3x^{2x+3}+e^2

Lösung

ableitung von

f (x) = 3 x^{2 x + 3} + e^{2}

3 x^{2 x + 3} (\frac{2 x + 3}{x} + 2 ln (x))

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (e^{2}) = 0

= 3 x^{2 x + 3} (2 ln (x) + \frac{2 x + 3}{x}) + 0

Vereinfache

= 3 x^{2 x + 3} (\frac{2 x + 3}{x} + 2 ln (x))

x \to 0 lim (e^{x} sin (x))

\int \frac{2}{x ( x ^{2} + 1 )} d x

\int y x^{2} d y

\frac{\partial}{\partial x} (3 x + 2 y)

\int \frac{x ^{2} + x - 5}{2 x ^{3} + 3 x ^{2} - 2 x} d x