1) The document discusses differentiation techniques such as differentiating polynomials, composite functions, and logarithmic and exponential functions. 2) It also covers applications of differentiation like finding maxima and minima, rates of change, and using differentiation to approximate small changes. 3) The key concepts covered are the derivative, differentiation rules, the relationship between the derivative and tangents/normals to curves, and using the derivative to solve optimization problems.

1. DIFFERENTIATION BY : PN. DING HONG ENG SM SAINS ALAM SHAH, K.L. PROGRAM MKS ADDITIONAL MATHEMATICS

2. SPM PAST YEAR QUESTIONS

3. FORM 4 2 1 2 2 1 1 07 1 07 1 1 07 2 1 1 1 2 07 1 1 06 1 1 06 1 06 3 1 1 1 3 06 1 1 05 1 1 05 1 1 05 3 05 1 1 Index Number 11. 1 2 2 Differentiation 9. 1 1 1 1 Circular Measures 8. 1 04 04 1 1 04 1 03 C 1 03 B 03 04 03 A 2 1 Solution of Triangles 10. Statistics Coordinate Geometry Indices and Logarithms 7. 6. 5. 1 1 2 2 Paper 2 Paper 1 Topics

4. FORM 4 2 1 2 06 06 06 3 1 1 1 3 06 1 1 05 1 1 05 1 05 3 05 1 1 Index Number 11. 1 2 2 Differentiation 9. 1 1 1 1 Circular Measures 8. 1 04 04 1 1 04 1 03 C 1 03 B 03 04 03 A 2 1 Solution of Triangles 10. Statistics Geometry Coordinates Indices dan Logarithms 7. 6. 5. 1 1 2 2 Paper 2 Paper 1 Topics

5. DIFFERENTIATION The first derivative The second derivative Product Rule, Quotient Rule Differentiate Composite Function APPLICATION OF DIFFERENTIATION Gradient of a curve Gradient of tangent Gradient of normal Equation of tangent Equation of normal maximum and minimum value/point The rate of change Small changes and approximation Differentiate ax n Addition /Subtraction of algebraic terms

6. y=f(x) Q(x 2 , y 2 ) P(x 1 , y 1 ) 0 x 1 x 2 y 2 y 1 Gradient of chord = When point Q approaches point P (i.e x 2 x 1 ) Then When x 2 x 1 ,  x 0 Then y=f(x) Q(x 2 , y 2 ) P(x 1 , y 1 ) 0 x 1 x 2 y 2 y 1 Q 1 Q 2 CONCEPT OF DIFFERENTIATION

7. Differentiation Technicques Differentiate ax n If y = a, a is a constant --- If y = ax, a is a constant--- If y= ax n , a is a constant --- (d) Differentiate Addition, Subtraction of algebraic terms. If , then

8. Differentiate Product/ Quotient of two Polynomials (a) If y = uv, then (b) If , then

9. Differentiate Composite Function If y = f(u) and u = g(x), then, the composite function or (ax+b) n = an(ax+b) n-1

10. The Second Derivative

11. The gradient of the curve y= f(x) at a point is the derivative of y with respect to x, i.e. or f’(x). Application of Differentiation 1. The gradient of tangent at point A is the value of at point A. 2. (Gradient of normal) x ( gradient of tangen) = -1 3. x y tangent normal

12. Equation of Tangent and Equation of Normal Equation of tangent at point (x 1 , y 1 ) with gradient m is y – y 1 = m ( x – x 1 ) Equation of normal at point (x 1 , y 1 ) is y – y 1 = ( x – x 1 )

13. Maximum and Minimum Point/Value At the turning point (stationary point), = 0 For maximum point < 0 For minimum point > 0 y x - - - - - - + + + 0 0 O

14. The Rate of Change If y = f(x), then is the rate of change of y with respect to time, t

15. SMALL CHANGES AND APPROXIMATION If y = f( x ) and is a small change in y corresponding with , a small change in x , then

16. SCORE A in Additional Mathematics

17. THANKS