need help on a math problem

[ChaoZ]

For the math people out there:
Find y' for y=7x/(x^3-1)^4

I already have the answer but I don't understand how to get it.

 

[Sukhoi]

chain rule

 

[hypn0tik]

Quotient Rule in conjunction with chain rule

if f(x) = g(x) / h(x) then f'(x) = [g'(x)*h(x) - g(x)*h'(x)]/ (h(x))^2

Here, g(x) = 7x and h(x) = (x^3+1)^4

You will need to use the chain rule for h'(x).

 

[ntdz]

Use the quotient rule.

So its the bottom times derivative of the top minus the top times the dervative of the bottom divided by the bottom squared...

I'm too lazy to do all the work out

 

[ChaoZ]

http://img220.imageshack.us/img220/8073/19jm.jpg

I don't know how to do the next step.

 

[PurdueRy]

Originally posted by: ChaoZ
http://img220.imageshack.us/img220/8073/19jm.jpg

I don't know how to do the next step.

simplify???

 

[chuckywang]

Product Rule with Chain Rule.

BTW, do NOT remember the quotient rule. It's not worth it. Just remember the product rule and chain rule.

 

[PurdueRy]

Originally posted by: chuckywang
Product Rule with Chain Rule.

BTW, do NOT remember the quotient rule. It's not worth it. Just remember the product rule and chain rule.

While the product rule is basically the chain rule, I would not tell anybody not to learn it. I learned it back in high school and I use it all the time in my daily hw.

 

[BigJ]

Originally posted by: chuckywang
Product Rule with Chain Rule.

BTW, do NOT remember the quotient rule. It's not worth it. Just remember the product rule and chain rule.

Low d Hi - Hi D Low
over
Low Low

How is that difficult or not worth it to learn?

 

[corpseofworms]

Ummm. . . you suggest he derives it from the product rule every time he needs it? Not sure about the real world, but my Calc 1 teacher (what I'm pretty sure he's in) drilled us pretty freaking hard on it. Just one more to remember on the list of differentiation rules.

 

[PurdueRy]

Originally posted by: corpseofworms
Ummm. . . you suggest he derives it from the product rule every time he needs it? Not sure about the real world, but my Calc 1 teacher (what I'm pretty sure he's in) drilled us pretty freaking hard on it. Just one more to remember on the list of differentiation rules.

All you would do is split the quotient into multiplication by a fraction...but that adds extra work in my mind

 

[ChaoZ]

Been studying all week and my brain is fried. Just can't comprehend this problem.

 

[hypn0tik]

Looks like you took the derivative correctly. From both the numerator and denominator, you can cancel out a (x^3-1)^3 term from top and bottom, leaving you with:

7(x^3-1) - 84x^3 in your numerator.

and (x^3 - 1)^3 in your denominator.

 

[PurdueRy]

Originally posted by: ChaoZ
Been studying all week and my brain is fried. Just can't comprehend this problem.

what trouble are you having about simplifying it after you have taken the derivative?

 

[hypn0tik]

What's the answer that they provide you with?

 

[ChaoZ]

http://img5.imageshack.us/img5/9513/15nc.jpg

Having trouble figuring out how to get from step 1 to step 2.

 

[mwtgg]

The answer should be [7/(x^3 - 1)^4] / [(84x^3)/(x^3 - 1)^5]

 

[PurdueRy]

Originally posted by: ChaoZ
http://img5.imageshack.us/img5/9513/15nc.jpg

Having trouble figuring out how to get from step 1 to step 2.

They just pulled out the 7(x^3-1)^4 since it was common to both terms in the numerator. The right side is what is left

In the denominator powers multiply...4*2=8

 

[Sukhoi]

Originally posted by: BigJ

Originally posted by: chuckywang
Product Rule with Chain Rule.

BTW, do NOT remember the quotient rule. It's not worth it. Just remember the product rule and chain rule.

Low d Hi - Hi D Low
over
Low Low

How is that difficult or not worth it to learn?

Low d Hi - Hi D Low
Draw the line
And square below

 

[ChaoZ]

For the answer I have : y' = 7(-11x^3 - 1) / (x^3 - 1)^5

 

[chuckywang]

Originally posted by: PurdueRy

Originally posted by: chuckywang
Product Rule with Chain Rule.

BTW, do NOT remember the quotient rule. It's not worth it. Just remember the product rule and chain rule.

While the product rule is basically the chain rule, I would not tell anybody not to learn it. I learned it back in high school and I use it all the time in my daily hw.

I think the product rule and the chain rule are pretty seperate. The quotient rule however, is a special case of the product rule.

 

[chuckywang]

Originally posted by: corpseofworms
Ummm. . . you suggest he derives it from the product rule every time he needs it? Not sure about the real world, but my Calc 1 teacher (what I'm pretty sure he's in) drilled us pretty freaking hard on it. Just one more to remember on the list of differentiation rules.

I suggest he uses product rule on (7x)*(1/(x^3-1)^4).

 

[Midlander]

Originally posted by: mwtgg
The answer should be [7/(x^3 - 1)^4] / [(84x^3)/(x^3 - 1)^5]

Dang. I thought the answer was Lucy Van Pelt.

 

[Mokmo418]

mistake somewhere i'll repost when i find out where it is

 

[RadioHead84]

you understand it now or should i give it a try at explaining as well?