Question

How do you use the chain rule to differentiate `f(x)=e^(3x)`?

Answer 1

`f'(x)=3e^(3x)`

Explanation:

If `f(x) = f(g(x))` then the Chain rule states that:

`f'(x) = f'(g(x))*g'(x))`

In this example: `f(x) = e^(g(x))` and `g(x) = 3x`

`:. f'(x) = e^(3x) * d/dx(3x) = e^(3x) * 3`

`= 3e^(3x)`