Question

How do you use the chain-rule to find the derivative of f(x) = a^x?

Answer 1

I believe you can use the identity:\[a^x=e^{\ln(a^x)}=e^{x\ln(a)}\]and then use the chain rule.

Answer 2

yes but how do I use the chain rule there

Answer 3

use the substitution:\[u=x\ln(a)\]so that:\[f=e^u\]then:\[\frac{df}{dx}=\frac{df}{du}\times\frac{du}{dx}\]