# find the Derivative

• Feb 26th 2008, 05:27 PM
bluejewballs
find the Derivative
Find the derivative
g(x)=2*11^(-x)

would you move 11^(-x) to the denominator and use product rule?
• Feb 26th 2008, 05:35 PM
mr fantastic
Quote:

Originally Posted by bluejewballs
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 $y = a^{kx}$.

Then $\ln y = \ln a^{kx} = kx \ln a \Rightarrow y = e^{(k \ln a) x}$.

Therefore $\frac{dy}{dx} = (k \ln a) \, e^{(k \ln a) x} = (k \ln a) \, y = (k \ln a) \, a^{kx}$.

Key result: If $y = a^{kx}$ then $\frac{dy}{dx} = (k \ln a) \, a^{kx}$.