**can someone answer : find dy/dx by implicit differentation, if y cos x = x sin y?**

**Answer:**

Use product rule and implicit differentiation,

product rule d/dx(uv) = u’v + v’u.

Hence your answer is given by,

dy/dx*cos(x) -y*sin(x) = sin(y) + x*dy/dx*sin(y) .

dy/dx*(cos(x) -x*sin(y)) = sin(y)*(1-y)

dy/dx= (cos(x) - x*sin(y))/(sin(y)*(1-y)).