*Note:- 1) If y = cosx ; then dy/dx = -sinx *

*2) If y = k ; where k = constant ; then dy/dx = 0*

*3) If y = u*v ; where both u & v are functions of 'x' , then*

*dy/dx = u*(dv/dx) + v*(du/dx)*

*4) If y = sinx ; then dy/dx = cosx*

Now, the given function is :-

4cos(x)*sin(y) = 1

Differentiating both sides w.r.t 'x' we get

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

or, dy/dx = [sin(x)*sin(y)]/[cos(x)*cos(y)]

or, dy/dx = tan(x)*tan(y)

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