# Find dx/dy by implicit differentiation. 4 cos x sin y =1

### 2 Answers | Add Yours

It is given that `4 cos x sin y =1` .

Take the derivative with respect to y of both the sides:

`(d(4 cos x sin y))/(dy) = (d(1))/(dy)`

=> `4*(-sin x)*(dx/dy)*sin y + 4*cos x*cos y = 0`

=> `4*sin x*(dx/dy)*sin y = 4*cos x*cos y`

=> `dx/dy = (4*cos x*cos y)/((4*sin x*sin y))`

=> `dx/dy = cot x*cot y`

**The derivative **`dx/dy = cot x*cot y`

4*(d/dx)[cosx*siny]=(d/dx)(1)

4[cosx*cosy*(dy/dx)-4siny*sinx]=0

4cosx*cosy*(dy/dx)-4siny*sinx=0

(dy/dx)=(siny*sinx)/(cosx*cosy)