Question

If `f(x)= 2x - e^x` and `g(x) = 3 x`, how do you differentiate `f(g(x))` using the chain rule?

Answer 1

`f'(g(x))=6- 3e^(3x)`

Explanation:

`f(g(x))=2*(3x)-e^(3x)`
can be written again
`f(g(x))=6x-e^(3x)`
use chain rule
differentiate "outside" function first, and then differentiate "inside" function
`d/dxf(g(x))`
=`f'(g(x))=6- **3** e^(3x)`
because 3x is "inside" function ，and it also need to differentiate