Higher Maths Differentiation Question

eirebhoy

Theres a example in my maths book which asks to diffrentiate Sin x from first principle. Theres a part of the solution wich I don't understand. Here it is:

[U]f(x+h)-f(x)[/U] = [U]2 Cos (x+1/2h) Sin (1/2h)[/U]
      h                      h

= 2 Cos (x+1/2h) . [U]Sin (1/2h)[/U] . [U]1[/U]
                     (1/2h)     2

How did he do the second line, shouldn't h be devided into everything?

eirebhoy

Sorry, I can't get the question organised but if you look in your text book you should see it. Hope you can help.

hussey

ok see this .. 9.2/h

that is the same as (9/1).(2/h)


so 2 cos (x+1/2h) is still being divided by h

as it is being multiplied by sin(1/2h) / h

Repli

[U]2 cos (x + h/2) sin (h/2)[/U]
              h
  

=

2 cos (x + h/2) [U]sin (h/2)[/U]
                 h

He is dividing everything by h

eg.

[U]6 x 4[/U]    = 6 x [U]4[/U]
  2            2

Hope this helps.. I suck at explainin stuff

PHB

Ok
The trick is that

h = 2h/2

and

When the limit of (Sin nx ) / n
goes to zero i.e. x-> 0

It becomes one

So the Sine becomes 1 and the h goes away leaving you with

Cosx

Hope i helped

eirebhoy

I get it now, thanks very much lads.

Also, Thanks to Seamus for sorting my post out for me, I now know how to use coding too.

Cheers.

seamus

Heh, I knew what it was supposed to look like, but couldn't remember for the life of me what was going on

And all that time I spent in 6th year wasted.........:p