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need help on a math problem

C

ChaoZ

Diamond Member
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.
 
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).
 
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 🙂
 
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.
 
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.
Click to expand...


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.
 
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.
Click to expand...

Low d Hi - Hi D Low
over
Low Low

How is that difficult or not worth it to learn?
 
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.
 
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.
Click to expand...


All you would do is split the quotient into multiplication by a fraction...but that adds extra work in my mind
 
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.
 
Originally posted by: ChaoZ
Been studying all week and my brain is fried. Just can't comprehend this problem.
Click to expand...

what trouble are you having about simplifying it after you have taken the derivative?
 
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.
Click to expand...

Low d Hi - Hi D Low
over
Low Low

How is that difficult or not worth it to learn?
Click to expand...

Low d Hi - Hi D Low
Draw the line
And square below
 
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.
Click to expand...


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.
Click to expand...

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

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