Question

Find dy/dx by the implicit differentiation

Answer 1

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

Answer 2

\[\frac{d}{dx} 4x^3 = 12x^2\]
\[\frac{d}{dx}x^2y = x^2\frac{dy}{dx} + y\frac{d}{dx}[x^2] = x^2\frac{dy}{dx} + 2xy\]
...
etc.

Answer 3

Where did you get stuck?

Answer 4

on the whole thing...my answer is saying wrong but I dont no what is wrong

Answer 5

You basically just want to take the derivative of each term on it's own, then solve for dy/dx.

Answer 6

What did you get when you took the derivative of each term? I can check that first, then move onto the algebra.

Answer 7

4x^3=12x^2

Answer 8

(x^2)y=x^2y'+2xy

Answer 9

xy^3=x3y^2+y^3

Answer 10

are you there?

Answer 11

Yes.

Answer 12

That third one isn't right.

Answer 13

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

Answer 14

did u see my answers

Answer 15

I did. The third one isn't right. You forgot your y' when you took the derivative of \(y^3\)

Answer 16

Did you figure it out from there?

Answer 17

no not yet...

Answer 18

So you have this:

\[12x^2 + x^2\frac{dy}{dx} + 2xy - 3xy^2\frac{dy}{dx} - y^3 = 0\]

And you want to solve for \(\frac{dy}{dx}\).. What is the first step?

Answer 19

why wud u do the dy/dx of x^2 again?

Answer 20

Because it was this:
\[\frac{d}{dx}[x^2y]\]Which from the product rule:
\[=x^2\frac{d}{dx}[y] + y\frac{d}{dx}[x^2]\]So we take the derivative of y with respect to x in the first term:
\[= x^2\frac{dy}{dx} + y(2x) = x^2\frac{dy}{dx} + 2xy\]

Answer 21

You aren't doing dy/dx of x^2. The dy/dx is multiplied by the x^2.

Answer 22

dy/dx is just y'.

\[=x^2y' + 2xy\]

Answer 23

i am completely lost now!