What did I do wrong on this implicit differentiation problem

Im supposed to find the slope of the tangent line at the point (3,2) for the function (4x^2+2y^2)^2-4x^2y=1864

So here's what I did

2(4x^2+2y^2)(8x+4yy')-4(2xy+x^2y')=0

(8x^2+4y^2)(8x+4yy')-8xy-4x^2y'=0

64x^3+32x^2yy'+32y^2x+16y^3y'-8xy-4x^2y'=0

y'(32x^y+16y^3-4x^2)=-64x^3-32y^2x+8xy

y'=(-64x^3-32y^2x+8xy)/(32x^2y+16y^3-4x^2)

So I plugged in the x and y values to get the slope but webwork says its incorrect, I thought I smacked the bullseye dead center but apparently I messed up somewhere... if anyone can take a look and see what mistakes I made I would appreciate it! Thank You!

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Re: What did I do wrong on this implicit differentiation problem

Quote:

Originally Posted by

**rhcprule3** Im supposed to find the slope of the tangent line at the point (3,2) for the function (4x^2+2y^2)^2-4x^2y=1864

So here's what I did

2(4x^2+2y^2)(8x+4yy')-4(2xy+x^2y')=0

(8x^2+4y^2)(8x+4yy')-8xy-4x^2y'=0

64x^3+32x^2yy'+32y^2x+16y^3y'-8xy-4x^2y'=0

y'(32x^y+16y^3-4x^2)=-64x^3-32y^2x+8xy

y'=(-64x^3-32y^2x+8xy)/(32x^2y+16y^3-4x^2)

So I plugged in the x and y values to get the slope but webwork says its incorrect, I thought I smacked the bullseye dead center but apparently I messed up somewhere... if anyone can take a look and see what mistakes I made I would appreciate it! Thank You!

Hello,

all your calculations are OK.

Unfortunately you didn't mention which result you've got. I got $\displaystyle y'=-\frac{512}{167}$

With the coordinates of the tangent point and this slope the equation of the tangent is

$\displaystyle y = -\frac{512}{167} \cdot x + \frac{1882}{167}$

For confirmation I've attached a sketch of the ellipse and it's tangent.

Re: What did I do wrong on this implicit differentiation problem

strange, i got -3.089 and i typed your answer in but its still incorrect.