Question

can someone please help me with this implicit differentiation problem? I have to find dy/dx or y'
xy^3 + 4x^2y^2-5xy=3x+2y

Answer 1

oy, thats just designed to give you tons of practice now isnt it ....

Answer 2

its just alot of product rules and power rules .... just have to keep track of it is all

Answer 3

haha yeah, i am horrrrible at them :/

Answer 4

xy^3, x'y^3+3xy^2y'
+4x^2y^2, 8xx' y^2+8x^2y y'
-5xy, -5x'y -5xy'
=
3x, 3x'
+2y, 2y'

since x' = dx/dx = 1, all those x' parts can be ignored

Answer 5

\[y^3+3xy^2y'+8xy^2+8x^2y y'-5y -5xy' = 3+2y'\]
gather your y's together and algebra it out

Answer 6

* your (y')s for clarity

Answer 7

haha i thinkkkk i solved it? does it equal (3+5y-8xy^2 -3y)/ (-2-5+8x^2y+3xy^2) ??

Answer 8

i dont see the y^3 in that setup

Answer 9

\[y^3+\color{red}{3xy^2y'}+8xy^2+\color{red}{8x^2y y'}-5y -\color{red}{5xy'} = 3+\color{red}{2y'}\]
\[\color{red}{3xy^2y'}+\color{red}{8x^2y y'}-\color{red}{5xy'}-\color{red}{2y'} = 3-y^3-8xy^2+5y\]
\[y'(\color{red}{3xy^2}+\color{red}{8x^2y}-\color{red}{5x}-\color{red}{2)} = 3-y^3-8xy^2+5y\]
\[y'=\frac{3-y^3-8xy^2+5y}{\color{red}{3xy^2}+\color{red}{8x^2y}-\color{red}{5x}-\color{red}{2} }\]

Answer 10

its just alot to keep track of ... :)

Answer 11

i finally got that but i got a -y^3 not -y^2 in the numerator?

Answer 12

xy^3 derives to y^3 + 3xy^2 y'

which is where the y^3 comes from

Answer 13

ohhh okay so the final answer is 3+ 5y-8xy^2-y^3)/(3xy^2+8x^2y-5x-3)?

Answer 14

3+ 5y -8xy^2 -y^3 tops good
-------------------
3xy^2 +8x^2y -5x -3 -2, not -3 on the end there

Answer 15

youuuu are a lifesaverrrrrrrr. (:

Answer 16

could you help me with onee more implicit differentiation problem?

Answer 17

i dunno, i had to dig deep just to get thru that one :)

Answer 18

hahaha