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)`