Question

How do you differentiate `y= 3^(2x+7)`?

Answer 1

Use `d/(dx)(a^x)=a^x ln a` together with the chain rule:

`d/(dx)(f(u))=f'(u) (du)/(dx)`

For `y=3^(2x+7)` we get:

`(dy)/(dx) = 3^(2x+7) ln3 (2) =2(3^(2x+7) ) ln3`

Or use `2ln3=ln9` to write:

`(dy)/(dx) = 3^(2x+7) ln9`