(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.

Started by Daniel Williamson, Mar 27 2006 07:51 PM

28 replies to this topic

Posted 21 April 2006 - 02:25 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.

HMFC - Founded 1874, beefing the Cabbage since 1875

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!

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

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!

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!

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.

Posted 23 April 2006 - 12:33 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!

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

Posted 23 April 2006 - 04:15 PM

hehe yep.

Posted 30 April 2006 - 07:33 PM

This thread scares me

And actually there is a semi-easy way to remember the difference (well I think so anyway!). For**i**ntegration you **i**ncrease the power and for **d**ifferentiation you **d**ecrease the power.

And actually there is a semi-easy way to remember the difference (well I think so anyway!). For

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