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

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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)

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial