Use this equation to find dy/dx. 4y cos(x) = x² + y²

Solution:

Given 4ycos(x) = x² + y²

This is an implicit function where we cannot write y in terms of x

By implicit differentiation, we get

d/dx {4ycosx} = d/dx (x² + y²)

4[dy/dxcosx + y(-sinx)] = 2x + 2ydy/dx

4[dy/dxcosx + y(-sinx)] = 2[x + ydy/dx]

2[dy/dxcosx - y(sinx)]= x + ydy/dx

2dy/dxcosx -2y(sinx)= x + ydy/dx

dy/dx[2 cos x -y]= x + 2y(sinx)

dy/dx = [x + 2y(sinx)]/[2 cos x -y]

Use this equation to find dy/dx. 4y cos(x) = x² + y²

Summary:

The value of dy/dx of 4y cos(x) = x² + y² is dy/dx = [x + 2y(sinx)]/[2 cos x -y].