Question

If (x^2/64)+(y^2/16)=1 and y(1)=3.97, find y'(1)

Answer 1

Have you considered an implicit derivative?

Answer 2

Yeah, it's just that this is summer homework and I don't really recall how to do it in this case.

Answer 3

I'd get 2x+2yy'=0, right?

Answer 4

It appears you DO remember how to do it. Good work.

Answer 5

Okay, so with y'= -x/y , I go back to the original equation to figure out what y was at that x value, and then I just plug in both values to the derivative equation?

Answer 6

Ooh, yup. Thank you so much! :)

Answer 7

You are given both values. It is assumed that y -s some function of x. Thus y(x) is given. In your case, y(1) = 3.97 and you have (1,3.97)