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Homework Help: calculus; implicit differentiation

Posted by Kim on Thursday, November 5, 2009 at 11:18pm.

Use implicit differentiation to find the slope of the tangent line to the curve at the point (4,1)

-1x^2 - 4xy + 3y^3 = -29

I differentiated both sides and solved for dy/dx and got 2x-4y/9y^2-4x. Then I plugged in X and Y and got -4/7

but when i enter my answer it's wrong. What is the right answer? Where did I go wrong?

• calculus; implicit differentiation - Reiny, Thursday, November 5, 2009 at 11:22pm

  I got (2x+4y)/(9y^2-4x) for dy/dx
  
  I bet your error was in the derivative of
  -4xy
  which is -4x(dy/dx) - 4y
  
  check your signs.
  

• calculus; implicit differentiation - Kim, Thursday, November 5, 2009 at 11:28pm

  Thanks a lot, it was the signs that was wrong.
  

• calculus; implicit differentiation - drwls, Thursday, November 5, 2009 at 11:29pm

  Differentiate both sides of the equation with respect to x, with y being a function of x.
  
  -2x -4y -4x*dy/dx +9y^2*dy/dx = 0
  dy/dx = [2x +4y]/[9y^2 -4x]
  When x=4 and y = 1, I get
  dy/dx = (8 + 4) /(9 - 16) = -12/7
  

• calculus; implicit differentiation - Kim, Thursday, November 5, 2009 at 11:37pm

  Thanks :)
  

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