Question

How do you find the derivative of `y = (3x + 1)^2`?

Answer 1

Use chain rule / Expand

Explanation:

Method 1
`y=(3x+1)^2`
Assume the function in the bracket as some other variable say t.
`t = 3x+1`
`dt/dx = 3`
`y = t^2`
`dy/dx = dy/dt * dt/dx`
`=2t*3`
`dy/dx=6(3x+1)`

Method 2
If you can expand everything and find the derivative

`y = (3x+1)^2`
`y = 9x^2+6x+1`
`dy/dx = 18x+6`
`dy/dx = 6(3x+1)`