Can you check and help me my maths worksheet (mainly differentiation)?

Original post by KingKumar

Can you tell me whether these are right or not:

(1 / (x+4)) + (2 / (x-4)) = (3x+4) / (x²-16) (simplest form?)

Differentiating x⁴+6x^1/2 = 4x³+x^-1/2

Differentiating (x+4)² / x = 2x+8

Differentiating y=x⁴+x^1/3+3 = 4x³+(1/3)x^-2/3

Learn how to use LaTeX

http://www.thestudentroom.co.uk/wiki/latex

(1) Yes
(2) You have lost a 3
(3) Nope - what were you thinking there
(4) Yes

Reply 2

Dilzo999

19

The simplest form is in the factored version so you should have left it at

\dfrac{3x+4}{(x+4)(x-4)}

Reply 3

OP

Original post by TenOfThem

Learn how to use LaTeX

http://www.thestudentroom.co.uk/wiki/latex

(1) Yes
(2) You have lost a 3
(3) Nope - what were you thinking there
(4) Yes

So for (2) I just missed out the 3 before the second x.
For (3) I changed it to (x^2 + 8x + 16) / x then I differentiated it to 2x + 8 / 1 = 2x + 8

Reply 4

OP

Original post by Dilzo999

The simplest form is in the factored version so you should have left it at

\dfrac{3x+4}{(x+4)(x-4)}

Ok, thanks. :smile:

Reply 5

Original post by KingKumar

For (3) I changed it to (x^2 + 8x + 16) / x then I differentiated it to 2x + 8 / 1 = 2x + 8

Have you learnt the quotient rule yet

OR

\dfrac{x^2 + 8x + 16}{x} = x + 8 + 16x^{-1}

Can you differentiate that ?

(edited 10 years ago)

Reply 6

cambo211

19

Original post by TenOfThem

Have you learnt the quotient rule yet

OR

\dfrac{x^2 + 8x + 16}{x} = x + 8 + x^{-1}

Can you differentiate that ?

You've lost a 16 along the way there.

Reply 7

Original post by cambo211

You've lost a 16 along the way there.

Easily corrected :smile:

Reply 8

OP

Original post by TenOfThem

Have you learnt the quotient rule yet

OR

\dfrac{x^2 + 8x + 16}{x} = x + 8 + x^{-1}

Can you differentiate that ?

1 - 1x^-2

How does 16/x = x^-1? No, I don't know the quotient rule - not part of the IGCSE.

Reply 9

Original post by KingKumar

1 - 1x^-2

How does 16/x = x^-1? No, I don't know the quotient rule - not part of the IGCSE.

See the edit :smile:

Reply 10

cambo211

19

Original post by TenOfThem

Easily corrected :smile:

It is

But, as I thought they would, they took your maths as gospel.

Reply 11

3 is wrong, divide terms by x or use quotient rule, or maybe product with negative powers.

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(edited 10 years ago)

Reply 12

OP

Original post by cambo211

It is

But, as I thought they would, they took your maths as gospel.

The maths elders are belittling me.

Reply 13

OP

Original post by TenOfThem

Have you learnt the quotient rule yet

OR

\dfrac{x^2 + 8x + 16}{x} = x + 8 + 16x^{-1}

Can you differentiate that ?

Just checking, x^-1 means dividing by x? If possible can you show me why that is?

1 + -16x^-2 ?

Reply 14

For the last question, remember the point is on C as well to get some simultaneous equations, or you can sub in the roots of the quadratic you get into the original equation to check which one is correct.

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Reply 15

Original post by KingKumar

Just checking, x^-1 means dividing by x? If possible can you show me why that is?

1 + -16x^-2 ?

By the definition of x^(-1). x^{-1}=\dfrac{x^0}{x^1} = \dfrac{1}{x}.

Posted from TSR Mobile

Reply 16

OP

Original post by majmuh24

For the last question, remember the point is on C as well to get some simultaneous equations, or you can sub in the roots of the quadratic you get into the original equation to check which one is correct.

Posted from TSR Mobile

Sorry, could you elaborate?

Reply 17