Question

Using the first principles, find the derivative of `y=(3-x)/sqrt(2-x)` at x=-2?

Answer 1

there is no derivative at that point: infinity by one side, out of domain by the other side

Explanation:

`y = (3 - x)(2 - x)^(-1/2)`

`y' = (-1) (2 - x)^(-1/2) + (3 - x) (-1/2)(2 - x)^(-3/2)(-1)`

`y' = - 1 / (2 - x)^(1/2) + (3 - x) / (2 * (2 - x)^(3/2))`

`y' = (-2* (2 - x)+ 3 - x) / (2 * (2 - x)* (2 - x)^(1/2))`

`y' = (x - 1) / (2 * (2 - x)* sqrt(2 - x))`