If y= x+y then find d y d x at x=0, y=1

Step-by-step solution

Given the equation y = x + y . Squaring both sides, we get y^2 = x + y . Differentiating both sides with respect to x , we obtain 2y dy dx = x + dy dx . Rearranging the terms to solve for dy dx , we have (2y - 1) dy dx = x . Thus, dy dx = x 2y - 1 . Substituting the given values x = 0 and y = 1 into the expression for dy dx , we get dy dx = 0 2(1) - 1 = 1 2 - 1 = 1 . Answer: 1