Question

If g(x)+xsin(g(x))= x^2 find g'(0)

Answer 1

Differentiating this expression:
g(x)+xsin(g(x))= x^2

g'(x) + sin(g(x)) + x.g'(x) cos(g(x)) = 2x

Now set x = 0 and we have

g'(0) + sin(g(0)) + 0 = 0

hence g'(0) = - sin(g(0))