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# Differentiation/integration

### #1

Posted 27 March 2006 - 07:51 PM

### #2

Posted 27 March 2006 - 08:02 PM

Differentiation is when the power is reduced, at higher level you only need to know basic differentiation and trig.

While in integration you raise the power by one and add an arbitary constant.

I believe derivatives and integrals of trig functions are given on the formula sheet in the Higher exam, which should help.

For the chain rule (if you've covered that), differentiating gives:

(not sure if this is right, need to double check with someone else.

Integrating gives:

Also, consult the HSN notes on integrating and differentiating, if you need help.

Differentiation

Integration

Further Calculus

These notes provided on this website are excellent, providing many worked examples to go along with them. What you should do is pracise plenty of integration and differentiation questions until you get the hang of which is which.

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### #3

Posted 08 April 2006 - 12:33 PM

jus noticed this...one of the teachers in my school came up with a lame method, but anyway

Integration

Add

Divide

Differentiation

Multiply

Subtract

dunno how you would remember that in the exam tho :S

### #4

Posted 08 April 2006 - 12:52 PM

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### #6

Posted 09 April 2006 - 10:13 PM

i have just done enough of them to know what to do when i see one, i think its the safest way to do it, rather than learning some little saying....

### #7

Posted 09 April 2006 - 11:20 PM

probably doesnt help you but it give everyone an insight into how my head is wired...scarey eh

If i am not here i am somewhere else

### #9

Posted 10 April 2006 - 01:15 PM

### #10

Posted 10 April 2006 - 02:48 PM

There are no easy answers in Higher Maths, unless you practice or are a natural mathematician.

I really don't like maths, but you just have to practice. See it as a month until you never have to do maths again in your life! That's keeping me going!

### #11

Posted 13 April 2006 - 05:02 PM

### #12

Posted 13 April 2006 - 05:44 PM

If i am not here i am somewhere else

### #13

Posted 13 April 2006 - 06:31 PM

A tip for you:

There are no easy answers in Higher Maths, unless you practice or are a natural mathematician.

I really don't like maths, but you just have to practice.

**See it as a month until you never have to do maths again in your life!**That's keeping me going!

Unless you're foolish enough (like me) to take AH maths

### #14

Posted 20 April 2006 - 05:27 PM

### #15

Posted 20 April 2006 - 06:48 PM

### #16

Posted 20 April 2006 - 09:05 PM

You should differentiate from first principles. Oh aye. Take 5 hours to do the Higher math exam but that way you understand what you're doing.

### #17

Posted 20 April 2006 - 09:39 PM

### #18

Posted 20 April 2006 - 10:00 PM

They should teach the chain rule, or atleast mention the fact that you're multiplying by the derivative of the inner bracket.

Definitely, but most of the time it's sufficient to use the 'special version' of the chain rule, i.e. .

I would always read the

*a*as the "derivative of the bracket" though.

I'm not so sure about differentiation from first principles. It is good to introduce, and have a go at, but - particularly at Higher - you can only take it so far because most of the time, the computations are far too involved (have you ever tried it with sinx? ) That's the very reason why we have things like the chain rule!

### #19

Posted 21 April 2006 - 12:18 PM

They should teach the chain rule, or atleast mention the fact that you're multiplying by the derivative of the inner bracket.

Definitely, but most of the time it's sufficient to use the 'special version' of the chain rule, i.e. .

I would always read the

*a*as the "derivative of the bracket" though.

I'm not so sure about differentiation from first principles. It is good to introduce, and have a go at, but - particularly at Higher - you can only take it so far because most of the time, the computations are far too involved (have you ever tried it with sinx? ) That's the very reason why we have things like the chain rule!

I've never used that formula before, I always substituted part o the function with another function u and said The rest of my class does it that way but I was teaching myself at this point and this was the way they done it in the textbook, I guess its better for me because it seems like less of a pointless operation and I think you can see the reasoning behind it better.

By the way, does anyone know why the stuff from the code seems to have a bit chopped off at the bottom?

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