Find the derivative

g(x)=2*11^(-x)

would you move 11^(-x) to the denominator and use product rule?

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- Feb 26th 2008, 05:27 PMbluejewballsfind 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 PMmr fantastic
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 $\displaystyle \frac{dy}{dx} = (k \ln a) \, a^{kx}$.