Question

How do you find the derivative of `y=(3x+4x-x^2)^(1/2)`?

Answer 1

`(2-x)/(sqrt(3+4x-x^2))`

Explanation:

Did you mean this?

`(3+4x-x^2)^(1/2)`
I will be going off of that one for now.

Calculation

Apply chain rule:
`1/2(3+4x-x^2)^{-1/2}\times(4(1)-2x)`
`=1/(2(3+4x-x^2)^(1/2)]\times(4-2x)`
`=(4-2x)/(2(3+4x-x^2)^(1/2)`
`=(2(2-x))/(2(3+4x-x^2)^(1/2))`
`=(2-x)/(sqrt(3+4x-x^2))`