Differentiation

 
 

Derivatives







Learning Objectives

 Resources

DIFFERENTIATION  
 Limits from graphs 
 Limits from functions LIMIT FROM FIRST PRINCICPLES
 Limits x tends to infinity
 Applications of limits IMPORTANT LIMITS
 Continuity from graphs

 Gradient function GRADIENT FUNCTION
 Differentiation from principles
 DIFFERENTITION FROM PRINCIPLES
 Differentiation from graph SLOPE OF TANGENT

GRADIENT FUNCTION
 EXTENSION EXERCISE 5
 
 DIFFERENTIATION
 
 Differentiate Polynomial functions DIFFERENTIATE POLYNOMIALS
 Differentiate Composite functions CHAIN RULE
 Exponentials  e^(1/x),2e^(5x),etc DIFFERENTIATE EXP
 Composite logs 2ln(4x2), ln(sqrt(1-x/1+x)) DIFFERENTIATE LN(KX)
 Applications 
 Products x2(2x+1) PRODUCT RULE
WHY?
 Quotient (x+1)/(x-3)
 Exponentails and others 
 Logs and others 
 Trigonometrics sin(5x) 
 Inverse trig sec(x) 
 Inverse trig composite sec(2x) 
 Trig & products xsin(x) 
 Trig & quotients x/sin(x) 
Mixed

EXTENSION EXERCISE 6, 7, 8, 9

 CALCULUS AND CURVE PROPERTIES 
 Increasing & decreasing functions INCREASING AND DECREASING
 Maximun & minimun MAXIMUN/MINIMUN
 Second derivative SECOND DERIVATIVE TEST
 Stationary point STATIONARY POINTS
 Points of inflection
 CRITICAL POINTS
 Applications VOLUME OF A BOX
 Applications maximun & minimun ASYMPTOTES RATIONAL FUNCTION
 Model function
 
 
 
 Kinematics VELOCITY AND ACCELERATION

POSITION VS TIME GRAPHS

THE MOVING MAN(COOL APP)
 Gradient at a point,tangents & normals TANGENT PARALLEL TO LINE
EXTENSION EXERCISE 10,11,12
 I WILL DERIVE SONG
 IMPLICIT & PARAMETRIC DIFFERENTIATION
 
 Implicit differentiation


 Related rates of change

 
 From cartesians to parametric

 
 
 

FROM CARTESIAN TO PARAMETRIC

  Intersection between parametric


 Differentiate parametrics


 Tangents & normals TAN AND NORMAL PARAMETRICS
 EXTENSION EXERCISE 13,14,15  

 
 
 
 
 
Subpages (1): Integration