Question

Have i done this correctly?

Answer 1

find the derivative of x^3 + y^3 = 6xy

Answer 2

by implicit differentiation?

Answer 3

\[\frac{ d }{ dx } (x^3) + \frac{ d }{ dx } (y^3) = \frac{ d }{ dx } (6xy)\]
so,
\[3x^2 + 3y^2 \frac{ dy }{ dx } = 6x \frac{ dy }{ dx } + 6y\]

Answer 4

and now i can find dy/dx

Answer 5

looks good so far

Answer 6

put the dy/dx on the same side and factor out

Answer 7

i do think it's

\[\frac{ 2y-x^2 }{ y^2 - 2x }\]

Answer 8

its what i got

Answer 9

looks good

Answer 10

now do they not want y in the equation?

Answer 11

well,another one:
x^3 + y^4 = 16 find \[y ^{''}\]

Answer 12

what?

Answer 13

no i have to only find dy/dx

Answer 14

idk sometimes the question wants you to make it only x's

Answer 15

anyway continue

Answer 16

i can do it from the equation x^3 + y^3 = 6xy i'll have to find y and then plug in that instead of y

Answer 17

yeah but only do it if the question says so XD i was just asking

Answer 18

d/dx (x^4) + d/dx (y^3) = 0

Answer 19

let me write whatever i've done...

Answer 20

now a couple things. in the thing you just wrote you changed x^3 to x^4 and same with y
and it should be d/dy

Answer 21

and x^4 + y^4 = 16 so it would be
- 32 x^2/y^7

Answer 22

im not sure what is the correct equation.... is this new one the correct one?

Answer 23

are both the exponents 4?

Answer 24

what do you mean?

Answer 25

first you wrote x^3 + y^4

Answer 26

then you wrote x^4 + y^3

Answer 27

sry i made a mistake,the equation which i had to find y'' was x^4 + y^4 = 16

Answer 28

okay

Answer 29

be careful on the one where you took out -3 the sign on the INSIDE should change to negative

Answer 30

but you fixed it on the next part? so i guess you are okay

Answer 31

oh ok,

Answer 32

well thank you ;)

Answer 33

oh and the one you typed has an extra 2

Answer 34

you wrote -32
but your answer in the picture is perfect

Answer 35

sry - 48

Answer 36

?

Answer 37

i should have written x^4 + y^4 = 16 so (-3)(16) x^2 / y^7 and (-3)(16) = -48 but i wrote 32 and it's not correct ...

Answer 38

-48x^2 / y^7
perfect!

Answer 39

Thank you very much!