Warning: Illegal string offset 'html' in /home/hsn/public_html/forum/cache/skin_cache/cacheid_1/skin_topic.php on line 909

Differentiation/integration - HSN forum - Page 2

# Differentiation/integration

28 replies to this topic

Top of the Class

• Members
• 390 posts
• Location:Cambridge
• Interests:Muzak.
• Gender:Male

Posted 21 April 2006 - 02:25 PM

QUOTE(dfx @ Apr 21 2006, 03:02 PM)

QUOTE(George @ Apr 20 2006, 11:00 PM)

(have you ever tried it with sinx? )

Oh yes I was recently challenged by my maths teacher to differentiate from first principles. I believe it involves the taylor and maclaurin expansions for Sinx... but yeah I gave up lol.
You can do it with higher maths material. The only identities you need are:

HMFC - Founded 1874, beefing the Cabbage since 1875

### #22dfx

Fully Fledged Genius

• Members
• 1,955 posts
• Gender:Male

Posted 21 April 2006 - 03:03 PM

Yes the but I'm pretty sure you still need the taylor and maclaurin series... however I stand corrected!

Top of the Class

• Members
• 390 posts
• Location:Cambridge
• Interests:Muzak.
• Gender:Male

Posted 21 April 2006 - 04:54 PM

I'm not even going to pretend I know what they are
HMFC - Founded 1874, beefing the Cabbage since 1875

### #24George

Child Prodigy

• 720 posts
• Location:West Lothian
• Gender:Male

Posted 22 April 2006 - 01:21 PM

Here's the way I approached it:

However, that relies on two facts, and . The sinx / x limit requires a lot of work if you're being rigorous, and the cos limit follows from that quite easily.

Now, in practice, nobody would do all that work every time they needed to differentiate sinx!

The whole point of maths is to come up with theorems and rules. Once they're proved, it makes sense to just use the result - there's no point reinventing the wheel all the time!

### #25dfx

Fully Fledged Genius

• Members
• 1,955 posts
• Gender:Male

Posted 22 April 2006 - 02:43 PM

I was puzzling over why you delved into Cosh and Sinh when I realized it was h for height.

Top of the Class

• Members
• 390 posts
• Location:Cambridge
• Interests:Muzak.
• Gender:Male

Posted 23 April 2006 - 12:33 PM

QUOTE(George @ Apr 22 2006, 02:21 PM)

Here's the way I approached it:

However, that relies on two facts, and . The sinx / x limit requires a lot of work if you're being rigorous, and the cos limit follows from that quite easily.

Now, in practice, nobody would do all that work every time they needed to differentiate sinx!

The whole point of maths is to come up with theorems and rules. Once they're proved, it makes sense to just use the result - there's no point reinventing the wheel all the time!
This is also how I done it, except I didn't know how to calculate the limits myself and had to cheat a little with them.

dfx, h is meant to represent a small change in x, that's why the differentiated function is f(x+h) - f(x) / h - i.e. the change in f(x) over a change in x. Obviously the most accurate formula for the gradient will come as h is closer to zero.
HMFC - Founded 1874, beefing the Cabbage since 1875

### #27dfx

Fully Fledged Genius

• Members
• 1,955 posts
• Gender:Male

Posted 23 April 2006 - 04:15 PM

hehe yep.

### #28Vyka

Showing Improvement

• Members
• 12 posts
• Location:North east scotland
• Gender:Female

Posted 28 April 2006 - 01:45 PM

QUOTE(Daniel Williamson @ Mar 27 2006, 08:51 PM)

Any easy ways to remember the difference between the two? add one to power divide by new power i mean come on

PRACTICE!!! Just like the rest of us hahaha

### #29ScotlandGirl

Good Effort

• Members
• 86 posts
• Gender:Female

Posted 30 April 2006 - 07:33 PM