Question

need help with the attached problem

Answer 1

\[y^2-2xy+3=0\]? is that it?

Answer 2

wow you are already on"implicit differentiation"

Answer 3

I guess my calculus professor at UT Austin is going really fast, lol

Answer 4

so we want the derivative of this thing with respect to x
the derivative of
\[y^2\] is
\[2yy'\] and the derivative of
\[-2xy\] requires the product rule. the derivative of 3 is 0 so we are almost done

Answer 5

first of all is it clear that the derivative of
\[y^2\] is
\[2yy'\]?

Answer 6

it is like saying that the derivative of
\[f^2(x)=2f(x)f'(x)\] we are thinking of y as a function of x, but we haven't actually written it as one

Answer 7

ok

Answer 8

the derivative of
\[-2xy\] is
\[-2(y +xy')\]

Answer 9

that is the "product rule" like saying the derivative of
\[xf(x)\] is
\[f(x)+xf'(x)\]

Answer 10

so your equation for the derivative is
\[2yy'-2y-2xy'=0\]

Answer 11

now we can use algebra to solve for
\[y'\] or if you like you can actually at this step replace x and y by 2 and 1

Answer 12

second method may be easier. you get
\[2\times 1\times y'-2\times 1-2\times2y'=0\]
\[2y'-2-4y'=0\]
\[-2y'-2=0\]
\[-2y'=2\]
\[y'=-1\]

Answer 13

any step not clear let me know

Answer 14

All the steps are clear, but I'm going to need to do some more problems on this so I can get the hang of it

Answer 15

Thanks!

Answer 16

it is best to think of
\[y=f(x)\] and keep applying the chain rule. then you will have a bunch of y' in your answer

Answer 17

ok, thanks for the tip