Posted by Kim on .
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,
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,
Thanks a lot, it was the signs that was wrong.

calculus; implicit differentiation 
drwls,
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,
Thanks :)