If sqrt x +y + sqrt y-x = c, then d^2y/dx^2 is equal to - Maths - Continuity and Differentiability

Question

If sqrt x +y + sqrt y-x = c, then d^2y/dx^2 is equal to

Manbar Singh · Accepted Answer

We have,     x+y + y-x = c⇒x+y + y-x2 = c2⇒x+y+y-x+2y2-x2 = c2⇒2y + 2y2-x2 = c2⇒2y2-x2 = c2-2y⇒4y2-x2 = c4+4y2-4c2y⇒4y2 - 4x2 =  c4+4y2-4c2y⇒-4x2 = c4-4c2y⇒4c2y = c4+4x2Differentiating with respect to x, we get    4c2×dydx = 8x⇒dydx = 8x4c2⇒dydx =2xc2Differentiating again with respect to x, we getd2ydx2 = 2c2

If sqrt x +y + sqrt y-x = c, then d^2y/dx^2 is equal to.