1.

If y + x = sin(y + x) then find dy/dx.

Answer»

According to, y + x = sin-1(x + y)

Differentiating w.r.t. x, 

(dy/dx) + (dx/dx) = (d sin(x + y)/d(x + y)) x (d(x + y)/dx)

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

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

{1 - cos(x + y)}(dy/dx) = cos(x + y ) - 1

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

dy/dx = 1


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