If x + y = xy, then dy/dx = Please explain step by step.

Expert Answers

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

Given the equation.

x + y= xy

We need to find dy/dx

We will use implicit differentiation.

==> (x+y)' = (xy)'

==> x' + y' = (x)y' + x'(y)

==> 1 + y' = xy' + y

Now we will combine terms with y' on the left side.

==> y' - xy' = y-1

==> y'(1-x)= y-1

==> y'= (y-1)/(1-x)

==> dy/dx = (y-1)/(1-x)

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