Question

Cum se calculează, derivata?
f'(x)=
$x \times 4 {}^{x - 1}$

Answer 1

$\text{Mai intai hai sa calculam derivata lui }4^{x-1}.\\ (4^{x-1})'=(4^x \circ (x-1) )'=((4^x)'\circ(x-1))\cdot (x-1)'=4^{x-1}\cdot \ln 4\\ f'(x)=x'\cdot 4^{x-1}+(4^{x-1})'\cdot x=4^{x-1}+4^{x-1}\cdot \ln 4\cdot x=\\ =\boxed{4^{x-1}(1+x\cdot \ln 4)}$