`4 cos(x) sin(y) = 1` Find `(dy/dx)` by implicit differentiation.

Textbook Question

Chapter 3, 3.5 - Problem 13 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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hkj1385 | (Level 1) Assistant Educator

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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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