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 2x4y/9y^24x. 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^24x) 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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