Implicit Differentiation: Finding dy/dt for x^2+3y^2+2y=10

[Iron_Brute]

I've been working on this problem for a while and can't see my mistake, in the book the answer is stated as being 3, but I end up getting 13.5.

Homework Statement

If x^2+3y^2+2y = 10; dx/dt = 2, x=3 and y = -1 find dy/dt

The Attempt at a Solution

d/dt[x^2+3y^2+2y] = d/dt[10]

3x^2 (dx/dt) + 6y(dy/dt) + 2 (dy/dt) = 0

6y (dy/dt) + 2 (dy/dt) = -3x^2 (dx/dt)

dy/dt (6y+2) = -3x^2 (dx/dt)

dy/dt = -3x^2 (dx/dt) / 6x+2

dy /dt = -3(3^2)(2) / 6(3)+2 = 13.5

 

[tiny-tim]

Hi Iron_Brute!

(try using the X² tag just above the Reply box )

If x^2+3y^2+2y = 10; dx/dt = 2, x=3 and y = -1 find dy/dt
…
3x^2 (dx/dt) + 6y(dy/dt) + 2 (dy/dt) = 0

erm …

either it's x³ in the question or it's 2x in the derivative

 

[Iron_Brute]

Hi Iron_Brute!

(try using the X² tag just above the Reply box )erm …

either it's x³ in the question or it's 2x in the derivative

Ugh I can't believe it, it's x^2 in the text but I wrote x^3 on my sheet. Thanks for the help (and the tip on writing the exponents didn't know that), I can't believe I spent so much time looking my problem over and didn't see that.