Finding the derivative using the chain rule

Question

I have been at this problem for and hour now, and i got 4 answers that were all wrong. I only have one attempt left on my homework, and I have no idea how to remanipulate it. At first i mistook it for a power function, then and expoenential, and now I figue it is a chain and exponential.

 

g(theta)=2*3^-theta

 

Please help me, I am so confused.

Answer 1

g(x) = 2 * 3^-x

 

This is an exponential function.  Take natural log of both sides:

 

ln g(x) = ln2 - x ln3

 

Take derivative of both sides using the logarithmic derivative and the chain rule:

 

g'(x) / g(x) = -ln3

 

Solve for g'(x):

 

g'(x) = g(x) (-ln3) = (2 * 3^-x) (-ln3)