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FURTHER FIRST PRINCIPLES DIFFERENTIATION

Page history last edited by Steph Richards 15 years, 3 months ago

WJEC SPECIFICATIONS FOR THIS TOPIC AT FP1

 

  TOPIC NOTES
6.

The general definition of a derivative.

Finding, from first principles, the

derivative of simple algebraic

functions.

 

LINKS TO WJEC FP1 PAST PAPERS 

 

Past Paper Question P5 2005 Emma Courtney

 

PAST PAPER QUESTIONS LINK TO CERYS RAND'S WIKI PAGE

 

FIRST PRINCIPLES DIFFERENTIATION- THE BASICS FROM C1

 

WORKED SOLUTION OF A PROBLEM (slightly harder than usual!)

 

 

Comments (4)

Kritikos5000and75 said

at 10:03 am on Jan 12, 2009

Thankyou!

Kritikos5000and75 said

at 6:22 pm on Jan 12, 2009

I understand the idea behind First Principles Differentiation but isn't there this single method of solution that applies to every type of problem? For instance; 3x^5-2x^3+4x..... I can solve it this way >>> 3(5x^5-1)-2(3x^3-1)+4x^1-1 <<< but I cannot solve it the way you have shown here. Thanks.

Steph Richards said

at 7:17 pm on Jan 12, 2009

You are now asking about powers of x which are higher than 2. This means that F(x+h) will involve (x+h) to a power higher than 2. The expansion of this would require the binomial expansion if you are using first principles. WJEC FP1 courses may require first principles expansions of cubics or reciprocals (as in the solution above) but I have not seen powers higher than 3. It depends if the requirements of your course need you to investigat powers of 5 as you question above. The main point is first principles differentiation is ALWAYS the same method, its the algebra involved in the manipulation of f(x+h) -f(x) that changes depending on the function. Trigonometric differentiation from first principles? now thats another story again!!!

Steph Richards said

at 7:19 pm on Jan 12, 2009

Have you looked at the two worked solutions of the two Hawthorn High school pupils (Linked above) worth a look.

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