Question

Use implicit differentiation to find an equation of the tangent line to the curve at the given point 2(x^2+y^2)^2=25(x^2-y^2) and the point (3,1)

I've been working on this problem for a long time now and I can't figure out where I'm going wrong.

Answer 1

find f'(x) first

Answer 2

isolate y

Answer 3

plug in x to find the slope of the tangent line

Answer 4

than write ur equation in the format of (y-y1) = m(x-x1)

Answer 5

I started by doing the power rule and getting (4x^2+4y^2)[2x+2y dy/dx]=25(2x-2y dy/dx) and then distributed,isolated dy/dx, etc, but my answer is wrong because they are getting a negative answer and from the derivative I get I wouldn't get a negative answer.

Answer 6

u sure u know the product rule?

Answer 7

g*f'+f*g'

Answer 8

correct

Answer 9

u know ur power and chain rules?

Answer 10

Yes I set it up correctly that I can see. It is in the few comments above this

Answer 11

well can i see ur isloated f(x)?

Answer 12

isolated*

Answer 13

I know it is wrong because the answer is negative and my dy/dx isn't going to give a negative answer but I got x/(8x^3+8x^2y+8y^2x+8y^3+y)

Answer 14

all of that equals y? hly smokes...

Answer 15

I mean that's what I got but I don't know. I don't see where I went wrong, I just know it isn't correct.

Answer 16

hmmm

Answer 17

ur y isn't isolated...

Answer 18

you are isolating dy/dx (the derivative of y with respect to x), not the y variable.

Answer 19

or y', it means the same thing

Answer 20

mhmm ok

Answer 21

gtg soon so can't solve the whole thing...

Answer 22

back to your previous post to see