derivative of x^{sqrt(x)}+2^xln(x)

Lösung

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

x^{x} (\frac{ln ( x )}{2 x} + \frac{1}{x}) + ln (2) \cdot 2^{x} ln (x) + \frac{2 ^{x}}{x}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= x^{x} (\frac{ln ( x )}{2 x} + \frac{1}{x}) + ln (2) \cdot 2^{x} ln (x) + \frac{2 ^{x}}{x}

\int \frac{x - 4}{x} d x

a re a x, x^{2} - 2, - 1, 4

x \to 4 lim (x + 2)

2 y \cdot sin (x) d x = cos (x) d y - 2 d x

\frac{\partial}{\partial y} (ln (3 x^{2} - y^{3} - 3))