Find the derivative
g(x)=2*11^(-x)
would you move 11^(-x) to the denominator and use product rule?
I'll do the general case:
Let $\displaystyle y = a^{kx}$.
Then $\displaystyle \ln y = \ln a^{kx} = kx \ln a \Rightarrow y = e^{(k \ln a) x}$.
Therefore $\displaystyle \frac{dy}{dx} = (k \ln a) \, e^{(k \ln a) x} = (k \ln a) \, y = (k \ln a) \, a^{kx}$.
Key result: If $\displaystyle y = a^{kx}$ then $\displaystyle \frac{dy}{dx} = (k \ln a) \, a^{kx}$.