Sebarkan ilmu .....: nota 1 - pembezaan

http://www.intmath.com

nota 1 - pembezaan

Asas rumusan pembezaan acu try sini : http://www.sosmath.com/tables/derivative/derivative.html

ini pun petikan daripada laman web...;-

First principles is also known as "delta method", since many texts use Δx (for "change in x) and Δy (for "change in y"). This makes the algebra appear more difficult, so here we use h for Δx instead. We still call it "delta method".
NOTE
If you want to see how to find slopes (gradients) of tangents directly using derivatives, rather than from first principles, go to Tangents and Normals in the Applications of Differentiation chapter.
We wish to find an algebraic method to find the slope of y = f(x) at P, to save doing the numerical substitutions that we saw in the last section (Slope of a Tangent to a Curve - Numerical Approach).
We can approximate this value by taking a point somewhere near to P(x, f(x)), say Q(x + h, f(x + h)).
The value is an approximation to the slope of the tangent which we require.
We can also write this slope as "change in y / change in x" or:
If we move Q closer and closer to P, the line PQ will get closer and closer to the tangent at P and so the slope of PQ gets closer to the slope that we want.
If we let Q go all the way to touch P (i.e. h = 0), then we would have the exact slope of the tangent.
Now, can be written:
So also, the slope PQ will be given by:
But we require the slope at P, so we let h → 0 (that is let h approach 0), then in effect, Q will approach P and will approach the required slope.
Putting this together, we can write the slope of the tangent at P as:
This is called differentiation from first principles, (or the delta method). It gives the instantaneous rate of change of y with respect to x.
This is equivalent to the following (where before we were using h for Δx):
You will also come across the following for delta method:

E2001 - matematik Kejuruteraan 2

Untuk topik PEMBEZAAN shj - bagi semester pendek pelajar pjk.

2. credit hours for E2001

Learning Out Comes for Topic Differentiation only.

2. Strengthen his/her understanding of basic differentiation for simple, trigonometric, logarithmic and exponential functions.

Summary

2. DIFFERENTIATION [6:3]

This topic includes first degree differentiation, multiplication and division functions, trigonometric, logarithmic and exponential functions. Differentiation concept is also applied in parametric equation functions.


SYLLABUS

2. DIFFERENTIATION

2.1. State the basic differentiation rule.
2.2. Derive and use of chain, product and quotient rule
2.3. State the basic differentiation formula for trigonometric, logarithmic and exponential functions.
2.4. Use of formula to differentiate the parametric equation functions.
2.5. Solve problems related to differentiation.

Assessment

Continuous evaluation (CE) – 50%
Final examination(FE) – 50%

Continuous evaluation (CE)

Quizzes – minimum of 5 [30%]
Assignments – minimum of 4[40%]
Test – minimum 2[30%]

Reference

Calculus (2nd Ed), Addison-Wesley Publishing Company.
Finite Mathematics : An Applied Approach (8th Ed). Ins. New York ; John Willey & Sons.
Engineering Mathematics; Programs And Problems (4th Ed). Macmillan Press Ltd.
Understanding Pure Mathematics, Oxford University Press.