Question

How do you differentiate `f(x)= (3e^x+2)^3` using the chain rule.?

Answer 1

`f'(x)=9e^x(3e^x+2)^2`

Explanation:

According to the chain rule
`f'(x)=3(3e^x+2)^2d/dx[3e^x+2]`

Calculate the inner derivative.
`d/dx[3e^x+2]=3e^x`

Plug back in.
`f'(x)=3(3e^x+2)^2xx3e^x`
`f'(x)=9e^x(3e^x+2)^2`