Find dp/dq using implicit differentiation:
2p^2*p*q=8p^2*q^2

Question

Find dp/dq using implicit differentiation:
2p^2*p*q=8p^2*q^2

lgbasallote · Answer

$$\large 2p^2pq = 8p^2q^2?$$

anonymous · Answer

yes that is right

anonymous · Answer

now how do i find the dp/dq of that equation using implicit differentiation?

lgbasallote · Answer

why dont you simplify first...

anonymous · Answer

would that be 4p*q?

anonymous · Answer

or p=4*q?

turingtest · Answer

second one

anonymous · Answer

so then what would the answer be?

turingtest · Answer

take the derivative with respect to q, then solve for dp/dq

anonymous · Answer

0?

turingtest · Answer

?

anonymous · Answer

would the answer be 0?

turingtest · Answer

no, the answer should be a function

turingtest · Answer

can you differentiate p=4q implicitly ?

turingtest · Answer

actually, in this case the answer is a number, but not 0

anonymous · Answer

4?

turingtest · Answer

yeah, I guess so
boring problem :S

anonymous · Answer

its saying 4 isnt right:(

callisto · Answer

1/4?

anonymous · Answer

also not correct :(

turingtest · Answer

that's the only was my other guess, but I am starting to suspect a typo

turingtest · Answer

then there is a typo

turingtest · Answer

I was suspicious of the way the problem was printed...

turingtest · Answer

unless differentiating implicitly means we can't simplify, which is not a rule I knew about

anonymous · Answer

its 2p^2-pq=8p^2q^2

anonymous · Answer

that is the correct problem.. not the one i posted before danm it

turingtest · Answer

dude, you have a 8 where there is a - sign

turingtest · Answer

a * I mean...

turingtest · Answer

so back to the drawing board :P

turingtest · Answer

$$ 2p^2-pq=8p^2q^2$$

anonymous · Answer

yes thats right

turingtest · Answer

I'll let Callisto do it...

anonymous · Answer

thanks for tryin to help tt

turingtest · Answer

no prob :)

callisto · Answer

Find dp/dq using implicit differentiation:
$$2p^2-pq=8p^2q^2$$$$p(2p-q)=8p^2q^2$$$$2p-q=8pq^2$$
Diff. both sides wrt q
$$\frac{d}{dq}2p-q=\frac{d}{dq}8pq^2$$$$2\frac{dp}{dq}-1=8q^2\frac{dp}{dq} + 16pq$$$$2\frac{dp}{dq}-8q^2\frac{dp}{dq}= 16pq+1$$$$(2-8q^2)\frac{dp}{dq}= 16pq+1$$$$\frac{dp}{dq}= \frac{16pq+1}{(2-8q^2)}$$
It doesn't look right... Does it?

anonymous · Answer

noo it isnt right ;/

callisto · Answer

@TuringTest Sir~ Please help!!~ :|

turingtest · Answer

something is rotten in the state of Denmark...
@Callisto I see no flaw in your reasoning, but perhaps there is a reason we can't simplify?
 I dunno, let me do it on paper...

turingtest · Answer

I get the same as @Callisto no matter how I slice it

anonymous · Answer

hmm maybe the problem is just a fluke who knows. i even tried an online calculator on it and it was saying that that answer it gave was also wrong while all the others i used it with came out correct  thanks for your help anyways guys!

callisto · Answer

What was the 'correct' answer??

callisto · Answer

@drumjockey83

anonymous · Answer

never found it out

turingtest · Answer

$$2p^2-pq=8p^2q^2$$$$4pp'-p'q-p=16p^2q+16pq^2p'$$$$4pp'-p'q-16pq^2p'=16p^2q+p$$$$p'(4p-q-16pq^2)=16p^2q+p$$$$p'={16p^2q+p\over4p-q-16pq^2}$$

turingtest · Answer

so maybe when we simplified that cause to q become a 1 when when we took the derivative though it wasn't supposed too?
I dunno, I wanna see why it makes a difference...

turingtest · Answer

I think that by simplifying we made it so we didn't have to use the product rule in the second term on the LHS, which caused us to drop the q
I guess we have to consider that p could be zero, and therefor we can't divide by it???

callisto · Answer

Does that mean we can't simplify the given equation before differentiating it?

turingtest · Answer

Not a rule I was familiar with, but I guess we'll know if/when @drumjockey83 tells us if this is the right answer now

anonymous · Answer

correct turning test ! thank you so much!

callisto · Answer

The answer tells us all......