Question

What is the implicit derivative of `1=y^2-5xy`?

Answer 1

`(dy)/(dx) = (-5y)/(5x-2y)`

Explanation:

Differentiate term by term. As `y(x)` is a function of `x` we must use the chain rule.

`d/(dx)(1) = d/(dx)(y^2) - d/(dx)(5xy)`

`0 = 2y(dy)/(dx) - 5y - 5x(dy)/(dx)`

Group like terms:

`(dy)/(dx)(5x-2y) = -5y`

`therefore (dy)/(dx) = (-5y)/(5x-2y)`