Question

Find dy/dx in terms of y when x and y are related by the following equation:
x=y−y^3

Answer 1

This is an implicit differentiation problem with a twist :D
But, more on that later...
Could you please differentiate both sides of the equation with respect to x?
(Pretty Please? :) )

Answer 2

is this right?\[1=1-3*y^2\]

Answer 3

Naaaahh
:D

You can differentiate y the way you differentiate x, but ALWAYS remember to place a dy/dx afterwards... remember, we're differentiating with respect to x, not y ;)

Answer 4

Here, I'll give you an example to follow :)
Say we have to differentiate
\[1=x^2+y^2\]with respect to x. That's easy, we differentiate the left (which is just a constant anyway) and the right...
\[0=2x+2y\frac{dy}{dx}\]

See the difference? With x^2, we differentiate normally, but with y^2, we sorta differentiate normally, except when we're done, we put a dy/dx after it :)

Now you try :>

Answer 5

1/1-3y^2

Answer 6

My connection sucks, but wouldn't it be 1=dy/dx-(3y²)dy/dx?

Answer 7

and then taking dy/dx as a common factor: 1=dy/dx(1-3y²)

Answer 8

Yeah, that's it, and then you can factor out that dy/dx, like this
\[1=\frac{dy}{dx}(1-3y^2)\]

And now, it's just a matter of isolating dy/dx, which...

Answer 9

dy/dx=1/(1-3y²)

Answer 10

as @AQEE had already mentioned :)
But it's good that you managed to arrive at the answer yourself :D

Nice job ^.^

Answer 11

thanks @PeterPan !

Answer 12

No problem :>