Question

Find dy/dx when sin(x+y)=x^2+y^2

Answer 1

Given: sin(x+y)=x^2+y^2

To find: dy/dx of given expression.

Solution:

• We have given sin(x+y)=x^2+y^2.

• Now differentiating both sides with respect to x, we get:

           cos(x + y)(1 + dy/dx) = 2x + 2y dy/dx

• Now simplifying this, we get:

           cos(x + y) + cos(x + y)dy/dx = 2x + 2y dy/dx

• Taking the terms of dy/dx on one side:

           cos(x + y) - 2x = 2y dy/dx - cos(x + y)dy/dx

           cos(x + y) - 2x = { 2y - cos(x + y) } dy/dx

           cos(x + y) - 2x / 2y - cos(x + y) = dy/dx

Answer:

         So dy / dx is equal to cos(x + y) - 2x / 2y - cos(x + y)