derivative f(x)=4^x-x^2+3ln(x)

Lösung

ableitung von

f (x) = 4^{x} - x^{2} + 3 ln (x)

ln (2) \cdot 2^{2 x + 1} - 2 x + \frac{3}{x}

Schritte zur Lösung

\frac{d}{d x} (4^{x} - x^{2} + 3 ln (x))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (4^{x}) - \frac{d}{d x} (x^{2}) + \frac{d}{d x} (3 ln (x))

\frac{d}{d x} (4^{x}) = ln (2) \cdot 2^{2 x + 1}

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

\frac{d}{d x} (3 ln (x)) = \frac{3}{x}

= ln (2) \cdot 2^{2 x + 1} - 2 x + \frac{3}{x}