Question

How do you find `dy/dx` by implicit differentiation of `x^2+y^2=36`?

Answer 1

`dy/dx = -y/x`

Explanation:

`d/dx(x^2+y^2) = d/dx36`

`=> d/dxx^2 + d/dxy^2 = 0`

`=> 2x + 2y(d/dxy) = 0`
(Applying the chain rule with `y` treated as a function of `x`)

`=> 2x+2ydy/dx = 0`

`=> 2ydy/dx = -2x`

`:. dy/dx = -x/y`