`x e^y = x - y` Find `(dy/dx)` by implicit differentiation.

Expert Answers

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

Note:- 1) If y = e^x ; then dy/dx = e^x

2) If y = x^n ; then dy/dx = n*x^(n-1) ; where 'n' = real number

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

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

Now, the given function is :-

x*(e^y) = x - y

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

x*(e^y)*(dy/dx) + (e^y) = 1 + (dy/dx)

or, [x*(e^y) - 1]*(dy/dx) = [1 - (e^y)]

or, dy/dx = [1 - (e^y)]/[x*(e^y) - 1]

Approved by eNotes Editorial Team
Soaring plane image

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