Differentiation from First Principles Worked Example

A worked example of differentiation of a quadratic from first principles. The question is from WJEC C1 Jan 2008.

Category:

Education

Tags:

• WJEC
• differentiation
• first
• principles
• C1
• Maths
• level

[sbtccc]

Would prefer to see 'h' used instead of dx.

Some students manage to factor x's out too and cant dinstinguish between x and dx

[MathsAtHawthorn]

No problem. Just imagine all the "delta ex" as being h. The first principles theory is exactly the same. "delta ex" (which I cant type here sorry) would have been the original used in Newtons first principles arguments. "delta" refers to a small increment. Hence "delta ex" is a small increment in the "ex". h is only used to simplify the argument for students who think "delta ex" means "delta" multiplied by "ex".

[Kritikos5000and75]

Thanks!

[MathsAtHawthorn]

Thank you for taking the time to leave a comment.

If you are interested in resources for A level Maths then have a look on my website. You are very welcome.

[Kritikos5000and75]

I tried to apply the method explained in the other video dealing with differentiation on the following equation: f(x)=2x+1/x^2 and I did not get the right answer. Could you tell me how to solve this? And (x+hx)^2=x^2+2hx^2+h^2x^2... why do you write it this way>>> x^2+2xhx+hx^2

[MathsAtHawthorn]

The differential that you require f(x)=2x+1/x^2 is a more complex one than the video covers. The video covers first principles of simple quads only. The function that you are after contains a reciprocal. The first principles formula is the same but the algebra involved is not quite so easy. Have a look on my web site and I will try to upload a solution. You will find the solution under FP1 (Further Pure Maths 1) and the topic will be further differentiation from first principles

[MathsAtHawthorn]

Also you are confusing notation. You can use letter h for the small increment or deltax (use greek symbol) but not hx. Have you seen the website yet? Request to be a user and then you can ask questions on the pages or upload your scanned solutions so I can have a better look at what you are doing

[bazzingalore]

Thank you SO SO MUCH!

This helped a lot!!

The explanation is very easy to understand, and I must add, you're voice is rather calming =)

You're the kind of teacher that makes the student fall in love with math! ^_^ Thanks again!! =)

[mathsathawthornhigh]

Glad it helped.

[4howardia]

still applies to university maths (studying engineering) as a quick recap! so easy to forget the simple things!

[ScottyV656]

@sbtccc yes the formula you and i like is the y=f(x+h)-f(x)/h

I strongly suggest to anyone that is doing this to learn the power rule anx^n-1 this will help you know if you have done the first priniclples right. But dont forget those first priniples to the anx^n-1 rule because you will need it later in life.

[balochan1]

Thanks

[25defalco]

Great teacher ... I didn't understand this in High School, i just understood it now, thanks a lot :)

[RaamG025]

(Y)

[Ruffkidsbv]

this video is brilliant, i understood the first principal instantly (all the other people either work it too fast or don't explain some of the steps) keep up the brilliant work

[jatras1234]

@MathsAtHawthorn thank you so much can you do more plz on other topics

[Bowenwww]

Great video. Thanks :)