2sin(x)cos(y)=1 find the first derivative

Question

2sin(x)cos(y)=1    find the first derivative

Answer 1

If we differentiate both sides with respect to x, and using the chain rule, we get

    2[cos(x)cos(y)+(-sin(y)y'sin(x)]=0

    Dividing both sides by 2 gives: cos(x)cos(y)-y'sin(y)sin(x)=0

    So, y'=cos(x)cos(y)/[sin(x)sin(y)]

    This can be simplified to y'=cot(x)cot(y)

Answer 2

Assuming y to be a function of x, use implicit differentiation (and product rule):

 

2 cos x cos y + 2 sin x (-sin y)(dy/dx) = 0.

 

Now solve for dy/dx