### Differentiation

#### Derivatives

 Learning Objectives Resources DIFFERENTIATION Limits from graphs Limits from functions LIMIT FROM FIRST PRINCICPLES Limits x tends to infinity LIMIT TO INFINITY 1LIMIT TO INFINITY 2 Applications of limits IMPORTANT LIMITS Continuity from graphs CONTINUITY FROM GRAPH Gradient function GRADIENT FUNCTION Differentiation from principles DIFFERENTITION FROM PRINCIPLES Differentiation from graph SLOPE OF TANGENTGRADIENT FUNCTION EXTENSION EXERCISE 5 L´HOPITAL´S RULE    USING GEOGEBRA VIDEO 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 RULEWHY? Quotient (x+1)/(x-3) QUOTIENT RULE SONG 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 DIFFERENTIATE TRIG FUNCTIONS 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 OPTIMISATION OPTIMISATION CAN PROBLEM   OPTIMISATION CAN PROBLEM 2 OPTIMISATION TRIANGLE INSIDE CIRCLE Kinematics VELOCITY AND ACCELERATIONPOSITION VS TIME GRAPHSTHE 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 IMPLICIT DIFFERENTIATION Related rates of change CONE PROBLEM RATESLADDER SLIDING RATES SPHERE INCREASING RATE From cartesians to parametric FROM PARAMTO CART FROM PARAM TO CART 2 FROM PARAM TO CART 3 SKETCH PARAM EQSFROM CARTESIAN TO PARAMETRIC Intersection between parametric INTERSECTION PARAMETRICS Differentiate parametrics DIFF PARAMETRICSSECOND DERIVATIVE Tangents & normals TAN AND NORMAL PARAMETRICS EXTENSION EXERCISE 13,14,15

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