Question

find dx/dy of x^2 + y^2 = 16

Answer 1

do you know chain rule ?

Answer 2

chain rule :

d/dy (x^2) = 2x dx/dy

Answer 3

the answer on the back of the book says -x/y. how do i get there?

Answer 4

did you get how
d/dy (x^2) = 2x dx/dy
??

Answer 5

no

Answer 6

ok, thats why i asked whether you already know the chain rule.

Answer 7

2x+2y*y'=0

Answer 8

if we take derivative of x^2 w.r.t x, then we get 2x
but by chain rule,
when we take derivative of x^2 w.r.t y
we get
x^2 dx/dy

so we now have

x^2 dx/dy + 2y = 0

isolate
dx/dy from here.

Answer 9

@hartnn so this is essentially
2x * x' + 2y = 0
x' = -y/x

Answer 10

I'm assuming that OP typed "dx/dy" as a typo. I think OP meant "dy/dx" as it corresponds to the answer in the back of the book, "-x/y".

Answer 11

dy/dx indicates with which respect to variable we are differentiating and in this case it's the y

dx/dy would be the x

Answer 12

dy/dx is -x/y
yes

x' = dx/dy = -y/x
which gives
dy/dx = -x/y too

if the answer is -x/y
then the question must be dy/dx