Question

Help! How do I calculate the derivative of y: xy^4+x^2y=x+3y

Answer 1

\[xy ^{4}+x^{2}y=x+3y\]

Answer 2

y4 + 4xy^3 dy/dx + 2xy +x^2 dy/dx = 1+ 3 dy/dx

Answer 3

I'd like to know how to do it. Can someone explain what to do with this sort of problem?

Answer 4

do u know product rule..

Answer 5

Yes

Answer 6

What am I supposed to do? I still don't know where to start.

Answer 7

You know of implicit differentiation?

Answer 8

Just derive them term by term.
Let me give you an example, in the right hand side.
The derivative of x+3y is simply 1+3y'

Answer 9

kind of

Answer 10

Oh, that's it?

Answer 11

Not yet. Can you do the derivative in the left hand side?

Answer 12

Yeah. Using the product rule?

Answer 13

Yeah. You can show me the result of your answer for clarification. :)

Answer 14

Alright, great! I'm working the problem out right now!

Answer 15

any updates?

Answer 16

I got 4xy^3+y^4+2x^3y=1+3y'

Answer 17

are you sure?

Answer 18

another thing: take note that derivative of y is y'

Answer 19

Oh, whoops, I multiplied in a place where I should have added. Now I got 4xy'^3+y'^4+2x^y'+x^2=1+3y'

Answer 20

Still no.
It should be: 4xy^3 y' + y^4 +2xy +x^2 y' = 1+3y'

Answer 21

Oh okay. I made some more typos in my last answer, whoops! but is that all there is? That's it?

Answer 22

Not yet of course.
You need to isolate y' and equate the remaining terms to it.