Question

Please Help, MEDAL WILL BE REWARDED!
Find dy/dx by implicit differentiation and
evaluate the derivative at the given point.
x^3+y^3=4xy+1, (2,1)

Answer 1

so whats derivative of x^3 ?
y^3 ?

Answer 2

its 3y^2 and then 3x^2

Answer 3

to get d/dx (y^3)
you need to use chain rule
know what that is ?

Answer 4

yes, so I would get 3y^2 again

Answer 5

no...
d/dx (y^3) = 3y^2 dy/dx

Answer 6

okay so do I plug in my numbers from there and solve?

Answer 7

on the right side you need product rule

Answer 8

okay hold on...I get 9y^2/x

Answer 9

wait how ?
on right,
d/dx (xy) = x dy/dx + y

Answer 10

Oh, okay, so I would get -3/x^2

Answer 11

where does that come from ? :O
i am lost

Answer 12

Well im using product rule, right? Or am I using it wrong?

Answer 13

If I use product rule d/dd I get 0

Answer 14

ok, let me take you term by term
d/dx x^3 = 3x^2

d/dx y^3 = 3y^2 dy/dx

d/dx 4xy = 4 (x dy/dx + y)

d/dx 1 = 0

Answer 15

okay so that's d/dx but I need dy/dx, so would I substitute this into my original equation?

Answer 16

yes, we need dy/dx when x=2, y=1
so keep dy/dx as it is only
and plug in values for x and y

Answer 17

okay...I would start 2^3+1^3=4(2)(1)+1 right?

Answer 18

where did dy/dx go ?

Answer 19

IDK im confused on what equation im using

Answer 20

3x^2 + 3y^2 dy/dx = 4 (x dy/dx + y)

x=2
y=1

Answer 21

okay so my final answer would be 3x^2+3y^2 d(1)/d(2)=4( 2 d(1)/d(2) +1)?? @hartnn

Answer 22

no...
i said keep dy/dx as it is

Answer 23

3 (2^2) +3(1^2) dy/dx = 4 (2* dy/dx+1)
find dy/dx from here

Answer 24

okay, I get 12+4 dy/dx=4(2dy/dx+1) which is 16 dy/dx =4(3dy/dx)

Answer 25

no...
12 +3 dy/dx = 8 dy/dx +4
12 -4 = (8-3) dy/dx
8 = 5 dy/dx
so. dy/dx = 8/5

Answer 26

oh I see what your did, I skipped a step in my calculations. Okay, thank you so much! Im going to work this out again and see if I can get it right without making mistakes! Thank you so much!!!

Answer 27

good!
welcome ^_^