Pure maths help!

Please can you help me with this question. I can't seem to find where I am going wrong.

f(x)=[(x+1)(x+9)] / [x]

Show that f'(x)= [(x+3)(x-3)] / [x²]

(edited 6 years ago)

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Reply 1

wiseguy99

I think the problem you are having is there isn't a question

Reply 2

Alexia_17

Original post by wiseguy99

I think the problem you are having is there isn't a question

Sorry the picture I had taken wasn't uploading for some reason.

Reply 3

RogerOxon

Original post by Alexia_17

Please can you help me with this question. I can't seem to find where I am going wrong.

f(x)=[(x+1)(x+9)] / [x]

Show that f'(x)= [(x+3)(x-3)] / [x²]

What have you tried?

I'd start by multiplying-out the top and dividing through, then differentiate.

Please post your working.

(edited 6 years ago)

Reply 4

Alexia_17

Original post by RogerOxon

What have you tried?

I'd start with the chain rule: f(x)=a(x)b(x), f'(x)=a'(x)b(x)+a(x)b'(x), or you could multiply out the top and divide through.

Please post your working.

So far all I have tried is to expand the bracket to get
x²+10x+9 all over x

But I dont how that gets and x² on the bottom. I don't think I know what you mean by the 'Chain rule'. We have only just started differentiation friday of last week.

Reply 5

EquinoxGee

So you divide all the terms by x, giving x+10+9x^-1

Then, you times this by x^2/x^2. (This is equal to 1, but times it anyway and you'll see.)

Then factorise the numerator to get (x+3)(x-3) as the numerator and x^2 as the denominator

Reply 6

TheManor

Original post by Alexia_17

try to simplify x²+10x+9 all over x and then differentiate term by term ....what do you get ?

Reply 7

Alexia_17

Original post by Chrisabraham

When you multiply it does it equal, (x^3 +10x^2 + 9^-2)/x^2

also why do you multiply it by x^2/x^2

Reply 8

Alexia_17

Original post by TheManor

try to simplify x²+10x+9 all over x and then differentiate term by term ....what do you get ?

1-9x^-2 ??

Reply 9

TheManor

Original post by Alexia_17

When you multiply it does it equal, (x^3 +10x^2 + 9^-2)/x^2

also why do you multiply it by x^2/x^2

there are a few ways to do this. You started off the right way and got x^2 + 10x + 9 all over x. Now you need to do the division i.e. divide each term in your numerator by x. Then differentiate term by term ..... I wouldn't put it over x^2 just yet ...... you can do that after differentiating ....

Reply 10

TheManor

Original post by Alexia_17

1-9x^-2 ??

this is correct .....now combine this using fractions .... clue : 1 is x^2/x^2 ....

Reply 11

Alexia_17

Original post by TheManor

So after the division I will get, x+10+9x^-1, right?

Then after differentiation you'd then get, 1-9x^-2?

Reply 12

TheManor

Original post by Alexia_17

So after the division I will get, x+10+9x^-1, right?

Then after differentiation you'd then get, 1-9x^-2?

yes correct. Now you have to do some algebraic re-arrangement with this to get the answer. Clue : 9x^-2 means 9/x^2 and 1 is actually x^2/x^2 ......

Reply 13

Alexia_17

Thank you all so much. I just have one more question, not differentiation, that I am stuck on and I was wondering if any of you could help?

A boy is tobogganing down a smooth slope inclined at 20 degrees to the horizontal. Find his acceleration, assuming resistances can be neglected

Reply 14

TheManor

Original post by Alexia_17

step 1 : draw a diagram and show the forces ..... the word "smooth" tells you something ....

Reply 15

TheManor

Original post by TheManor

step 1 : draw a diagram and show the forces ..... the word "smooth" tells you something ....

step 2 : consider the direction the boy is accelerating in and write the "equation of motion" for this i.e. use Newton's 2nd law or "F=ma" ....

Reply 16

Alexia_17

Original post by TheManor

step 1 : draw a diagram and show the forces ..... the word "smooth" tells you something ....

But what do you do about the mass of the boy?
smoothmeans there no friction...

Reply 17

TheManor

Original post by Alexia_17

But what do you do about the mass of the boy?
smoothmeans there no friction...

yes - there is no friction. Don't worry about the mass just now.

The boy is sliding down the slope. What is the size of the force that is acting on him down the slope (this is where your force diagram comes in handy) .....