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# Maths People Quick Q For You: watch

1. When differentiating fractions such as:

(x-2)(2x+1)
x^4

do u take the term at the bottom and multiply it by all terms at the top?

2. (Original post by s25s)
When differentiating fractions such as:

(x-2)(2x+1)
x^4

do u take the term at the bottom and multiply it by all terms at the top?

In this case I would expand the brackets and divide by x^4
3. expand the top then use the fact that if y=u/v where u and v are functions of the same variable (in this case x),
then dy/dx = (vu' - uv')/(v^2).

u' means the first derivative of u, and v' is the first derivative of v.
4. I would expand the brackets in the numerator, and rewrite the term in the denominator as (x^4)^-1

and then find the derivative...
5. (Original post by s25s)
When differentiating fractions such as:

(x-2)(2x+1)
x^4

do u take the term at the bottom and multiply it by all terms at the top?

Expand the numerator first then use the quotient rule:
I would expand the brackets in the numerator, and rewrite the term in the denominator as (x^4)^-1

and then find the derivative...
but then do you have to multiply all the numerator terms by x^-4?
7. use the quotient rule That's the easy way, post #5.
8. i dont know the quotient rule!
9. Post #5.
10. (Original post by ViralRiver)
Post #5.
No need for quotient rule. Expand brackets and divide by x^4. It's so easy it can be done in your head.
11. what did everyone get? i got:

-4x^-3 +9x^-4 +8x^-5

is this right?
12. (Original post by s25s)
but then do you have to multiply all the numerator terms by x^-4?
Expand then quotient rule.
13. (Original post by steve2005)
In this case I would expand the brackets and divide by x^4
yo that's not right. You mean multiply the top and bottom by x^-4 I think.
14. (Original post by s25s)
but then do you have to multiply all the numerator terms by x^-4?
nah.

use the product rule.

i.e

If the derivative of f(x) = g(x) h(x), then

f '(x) = g(x) h '(x) + h(x) g '(x)
15. (Original post by s25s)
When differentiating fractions such as:

(x-2)(2x+1)
x^4

do u take the term at the bottom and multiply it by all terms at the top?

Cheat : log both sides...
16. (Original post by Iapetus)
yo that's not right. You mean multiply the top and bottom by x^-4 I think.
This is an easy differentiation. Suppose we wanted to differentiate

17. (Original post by steve2005)
This is an easy differentiation. Suppose we wanted to differentiate

I'm aware of how to do it. Expand then use the quotient rule or bring the x^4 up and use the product rule.

Your explanation of dividing by x^4 makes zero sense to me which is why I quoted you, and you haven't included sufficient steps in your answer as well. You are basically just giving the answer away which doesn't benefit anyone
18. (Original post by steve2005)
In this case I would expand the brackets and divide by x^4
exactly, this is the easiest method to use. after all, it's C1 while the quotient rule is C3

job done
19. (Original post by Iapetus)
I'm aware of how to do it. Expand then use the quotient rule or bring the x^4 up and use the product rule.

Your explanation of dividing by x^4 makes zero sense to me which is why I quoted you, and you haven't included sufficient steps in your answer as well. You are basically just giving the answer away which doesn't benefit anyone
Your explanation of dividing by x^4 makes zero sense to me

I hope the following explanation helps.

There is no need to "I'm aware of how to do it. Expand then use the quotient rule or bring the x^4 up and use the product rule."
20. (Original post by steve2005)
I hope the following explanation helps.
Oh right!! Cancelling the x's How silly of me. Thanks.
You see, I understood your 'divide by x^4' to result in changing the denominator to x^8. I didn't mean to sound rude either , just matter-of-fact like since you told me that it's 'easy' yet I could already solve the problem... Peace.

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