Question

Question #a16fd

Answer 1

Use `d/dx(b^x) = b^x lnb` and the chain rule.

Explanation:

`b^x = e^(xlnb)`, so

`d/dx(b^x) = e^(xlnb) * d/dx(xlnb) = e^(xlnb) *lnb = b^x lnb`

For `f(x) = 3^(2x-4)`, apply the previous formula and the chain rule:

`f'(x) = 3^(2x-4) ln3 (d/dx(2x-4)) = 2*3^(2x-4) ln3`

So the exact value of `f'(2)` is `f'(2) = 2ln3`