simple C1 differentiation question

sorry about this, but these questions are bugging me, I can't figure out how to differentiate this (I can do the process just don't know where to start) any help would be greatly appreciated!

2x+3
-------
x

Thankyou!

Reply 1

Mr M

Study Forum Helper

Original post by matthew100

Can you rewrite this using indices so you no longer have a fraction to worry about?

Reply 2

matthew100

Original post by Mr M

Can you rewrite this using indices so you no longer have a fraction to worry about?

that's the bit im stuck on Mr M, i'm not sure how to times x through

Reply 3

whooshpaddy

Original post by matthew100

When you divide by x, you decrease the indices by 1, as you know the x is actually x^1.

So you have 2x+3, which you can read as 2x^1 + 3x^0, so when you divide by x, you decrease the indices on each part by one.

(edited 12 years ago)

Reply 4

usycool1

Original post by matthew100

You can write it as 2x/x +3/x. Then arrange it so that there are no fractions. Can you go on from there?

Reply 5

Mr M

Study Forum Helper

Original post by matthew100

that's the bit im stuck on Mr M, i'm not sure how to times x through

x^{-1}(2x+3) = ?

Reply 6

Crowbar

2x+3
-------
x

Make them seperate
2x/x + 3/x

When dividing the x the powers just take away from each other.
2x^1/x^1 = 2x^0 = 2
3/x^1 = 3x^-1 (the power becomes negative when it you bring it from the bottom of the fraction to the top.)

Now dy/dx.

Reply 7

matthew100

it says the answer should be 3x-^2 (when dy/dx has been done)

(edited 12 years ago)

Reply 8

TheGrinningSkull

Original post by matthew100

it says the answer should be 3x-1 (when dy/dx has been done)

Are you sure?

Reply 9

hhh123

I thought you would have used the quotient rule.........???!!

Reply 10

matthew100

Original post by TheGrinningSkull

Are you sure?

that's what it says in the back of my c1 book im working on ex 7E QG

Reply 11

Nokiacrazi

Original post by hhh123

I thought you would have used the quotient rule.........???!!

Edexcel C1 :smile:

Reply 12

matthew100

sorted it!
cheers everyone, I wasn't expecting to get so many replies that quickly! i've sorted it thankyou all so much :smile:

Reply 13

Crowbar

Original post by matthew100

it says the answer should be 3x-^2 (when dy/dx has been done)

That's right. Actually is should be negative so -3x^-2.

(edited 12 years ago)

Reply 14

TheGrinningSkull

Original post by matthew100

that's what it says in the back of my c1 book im working on ex 7E QG

Original post by Nokiacrazi

Edexcel C1 :smile:

Oh, well, unless you wrote the question wrong in the OP then this should be differentiating 3x^-1 +2 which differentiates to -3x^-2 or:
-3
-----
x^2

Original post by hhh123

I thought you would have used the quotient rule.........???!!

That is C3 and you wouldn't here because the Exs for the first term cancel out giving a constant. :smile:

Reply 15

hhh123

Original post by Nokiacrazi

Edexcel C1 :smile:

Ah I see! I am OCR C3!!!

Reply 16

Mr M

Study Forum Helper

Original post by hhh123

Ah I see! I am OCR C3!!!

I think quotient rule would have been a poor choice anyway. Many simple quotients can be differentiated directly (like this) or by using the product rule.

Reply 17

hhh123

Original post by Mr M

I think quotient rule would have been a poor choice anyway. Many simple quotients can be differentiated directly (like this) or by using the product rule.