Question

Implicit Differentiation.

Answer 1

\[y ^{5}-x ^{4}y+x ^{2}y ^{3}=1\]

Answer 2

What have you done so far?

Answer 3

g\[5y ^{4} \frac{ dy }{ dt }- 4x ^{3}\frac{ dy }{ dt }+3y ^{2}\frac{ dy }{ dt }=0\]

Answer 4

Is it ok for you if I use y' instead of dy/dx

Answer 5

yeah sure

Answer 6

alright let me do this quickly :P

Answer 7

ok thanks

Answer 8

\[y'(x) = \frac{ 2xy^3-4x^3y }{ x^4-3x^2y^2-5y^4 }\]

Answer 9

Well this is what I got as the answer

Answer 10

Could you explain that a bit for me? I don't really understand :/ when i first started the problem and got the 5y^4 part, was I on the right track?

Answer 11

Yes you were but remember when you see lets say "x^4y" you should immediately know that you have to use the product rule.

Answer 12

oh so in the problem, i would have to use product rule twice then?

Answer 13

yup yup

Answer 14

Try it out and tell me how you do.

Answer 15

and then we can figure out the problem and go step by step.

Answer 16

alrighty

Answer 17

i got the numbers on the correct sides on the equal sign, but i can't figure how to get y prime by itself because the three terms all have y prime