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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