Question

How do you use the chain rule to differentiate `y=(x+2)^4`?

Answer 1

`4(x+2)^3`

Explanation:

by chain rule, `d/dx(f(g(x)))=f'(g(x))*g'(x)`

for this problem,
`f(x)=x^4 and g(x)=x+2`
`f'(x)=4x^3 and g'(x)=1`

that means `d/dx(x+2)^4=4(x+2)^3*1=4(x+2)^3`