Question

How do you use the chain rule to differentiate `y=(4x+5)^5`?

Answer 1

`dy/dx=20(4x+5)^4`

Explanation:

Let `y=(u(x))^n`
Then `dy/dx=n(u(x)^(n-1))u'(x)`
Here `u(x)=4x+5`
`u'(x)=4`
and `y=u(x)^5`
So `dy/dx=5(4x+5)^4*4=20(4x+5)^4`