Use this equation to find dy/dx. 5y cos(x) = x² + y²

Solution:

Given 5y cos(x) = x² + y²

It is an implicit function which means we cannot write y in terms of x

Implicit differentiation means differentiating w.r.t one variable keeping the other constant.

5y(-sinx) + 5cosxdy/dx = 2x + 2ydy/dx

5cosxdy/dx - 2ydy/dx = 2x + 5ysinx

(5cosx - 2y)dy/dx = 2x + 5ysinx

dy/dx = (2x + 5ysinx) / (5cosx - 2y)

Use this equation to find dy/dx. 5y cos(x) = x² + y²

Summary:

dy/dx {5y cos(x) = x² + y²} = (2x + 5ysinx) / (5cosx - 2y)