Question

If g(x) = 3^(2x) then g'(2) is?

A. 81
B. 162ln3
C. 81/ln3
D. 6/ln3
E. 6lin3

Answer 1

$\bf a^{u(x)}\qquad \qquad \cfrac{df}{dx}=\cfrac{df}{du}\cdot \cfrac{du}{dx}\\\\ -----------------------------\\\\ g(x)=3^{2x}\qquad \qquad u=2x \\\\\\ \cfrac{dg}{dx}=3^uln(3)\cdot \cfrac{du}{dx}\implies \cfrac{dg}{dx}=3^{2x}ln(3)\cdot 2 \\\\\\ g'(2)=3^{2\cdot 2}ln(3)\cdot 2\implies g'(2)=2\cdot 81ln(3)\implies g'(2)=162ln(3)$