Question

How do you use implicit differentiation to find `(dy)/(dx)` given `sqrtx+sqrty=1`?

Answer 1

`y' =- sqrty/(sqrtx) = 1 - 1/(sqrtx)`

Explanation:

`d/dx( sqrtx+sqrty=1)`

`implies 1/(2sqrtx)+1/(2 sqrty) y' =0`

`y' =- sqrty/(sqrtx)`

`y' =- (1 - sqrt x)/(sqrtx)`

`y' = 1 - 1/(sqrtx)`