how do i implicitly differentiate (x^2)(y')

Question

amistre64 · Answer

product rule

anonymous · Answer

i know that, im confused on what the terms would be because of the y'

amistre64 · Answer

y' is just another function in its own right:

D[(x^2)(y')] = x'^2 y' + x^2 y''

                  = 2x y' + x^2 y''

amistre64 · Answer

is this a part of a bigger problem?

anonymous · Answer

yeah it is, i think i see this part now though....could the second part be: x^2 yy' ? or is that not the same

amistre64 · Answer

no, that is not the same; but i could have  better answer prolly if I knew the problem from the start

anonymous · Answer

haha, well the full question is 9x3 + x2y − xy3 = 8

amistre64 · Answer

$$9x^3 + x^2y − xy^3 = 8$$
$$D[9x^3 + x^2y − xy^3 = 8]$$
$$D[9x^3] + D[x^2y] − D[xy^3] = D[8]$$
$$27x^2 + 2xy+x^2Y − (y^3+3xy^2Y) = 0$$
$$27x^2 + 2xy+x^2Y − y^3-3xy^2Y = 0$$
$$ x^2Y -3xy^2Y = -27x^2-2xy+ y^3$$
$$ Y(x^2 -3xy^2) = -27x^2-2xy+ y^3$$
$$ Y = \frac{-27x^2-2xy+ y^3}{x^2 -3xy^2}$$
I used Y for y' just so it stands out, but is this good so far?

anonymous · Answer

yep, i actually can see that..i think, the problem i am working on breaks it into sections also so this is real helpful, ive been doing the problem and i have the same thing as you so far

amistre64 · Answer

and you want to derive it once more right?

anonymous · Answer

nope, thats it! thanks!

amistre64 · Answer

cool :)