Hello,

I was wondering if someone could show me how to do this?

Differentiate Value of

I can't figure it out

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- February 8th 2010, 11:08 AMwolfhoundNasty derivative
Hello,

I was wondering if someone could show me how to do this?

Differentiate Value of

I can't figure it out - February 8th 2010, 11:15 AMHallsofIvy
Do you mean "differentiate both sides of this equation with respect to x"? If so, since the left side is just a constant with respect to x, and , you will get . That equation is never true however.

If you mean "differentiate both sides of this equation with respect to a", then, since the right side is a constant with respect to a, and using the product rule and chain rule, .

If neither of those is what you mean, then I have no idea what you**do**mean. - February 8th 2010, 11:47 AMmabruka
The other posible thing going on is that we wants to differentiate both sides like when you do do normal substitution in integrals:

I am not sure either - February 8th 2010, 12:17 PMvince
- February 8th 2010, 12:26 PMwolfhound
Hello

The value of a= x^-2

yes I need to use the chain and product rule but all these exponents are mixing me up help,Please - February 8th 2010, 12:38 PMvince
just great...now u tell us. oh well, my work above was consistent with the ambiguity of your intial post.

- February 8th 2010, 12:48 PMwolfhound
Sorry I thought it made sense

Please show me - February 8th 2010, 01:08 PMvince
way too many little steps for typesetting through latex all the way through. at any rate, here is the setup:

you want

=

=

Differentiating that is easy but lengthy. - February 8th 2010, 01:41 PMwolfhound
Hi why raise x^8 to the power of 3,and not raise (x^6-1) to power of 3 aslo?

is it easier to leave the top in brackets? - February 8th 2010, 02:11 PMArchie Meade
Hi wolfhound,

Vince has simply left the numerator "written" as a cube,

since you can now apply the chain rule to it,

or simply multiply out

Was it your idea to substitute

in the beginning?

Or was that requested by the question?

You see, you can do things the short way using x,

then manipulating the fraction to a simpler manageable one as Vince did.

Or... use the messy substitution and get some good experience with the Chain Rule.

Let me know the drive of the question,

I can show you the way using the substitution if you want to play along with it. - February 9th 2010, 09:17 AMwolfhound
Hello Archie (Hi)

It wasn't my Idea to use a=x^-2

It was in the question,

I cant seem to get this answer ( 28 -66x^6+48x^12-10x^18)/x^29

Is it best to use the product+chain rule, or chain+quotient rule?

Please help

Thanks - February 9th 2010, 02:08 PMArchie Meade
Hi wolfhound,

Since you have a product after your substitution,

you need to use a combination of product and chain rule.

It's much faster to do it the way Vince showed.

Nevertheless, here's what to do with the "a" substitution...

Putting all these together

We can write all of these terms using x to get the answer you are seeking.

Therefore the derivative is

- February 10th 2010, 07:06 AMwolfhound
Thanks Archie,

you really are my saviour !(Clapping)