Question

How do you differentiate `f(x) = (3x+7)^5?` using the chain rule?

Answer 1

`f'(x)=15(3x+7)^4`

Explanation:

`f(x)= (3x+7)^5`

Chain rule: `f(g(x))= f'(g(x))*g'(x)`

`f'(x)= 5(3x+7)^(5-1)*d/dx(3x+7)`

`=5(3x+7)^4 (3)`
`=15(3x+7)^4`