New Day 15

Chain Rule Easy

Chain Rule Intermediate

Chain Rule Harder Problems
Implicit functions and its differentiation   Imp.Diffn Ex1   Ex2  Ex3  Ex4  Implicit differentiation

Day 14

You should also memorize (x)'=1;  (√x)' =1/2√ x

Videos on differentiation (same as Day 13- to watch 10~14)

New Day 13

DERIVATIVES USING DEFINITION

Task 1.Watch the slides show and the videos links  in it DERIVATIVES 2 slide show

*Try answer what is the graphical significance of differential quotient and derivative (tangent/secant etc..) ?

*What is the general approach to getting the derivative of a function?

QUICK REVIEW

MEMORIZE DERIVATIVE OF BASIC IMPORTANT FUNCTIONS

f(x) = c,( where c is a constant), xⁿ,  ln x, e^x, sin x and cos x
All  derivatives of a function can be obtained from the below mentioned .

The videos below is an introduction to differentiation rules and how to use them.

Videos on differentiation

Day 12

SLOPE EXERCISES on Derivatives

Slide on derivative curves-understanding

TIP:In the problems below  the idea should be to not get lost in increasing/decreasing shapes of the derivative graph,but to concetrate on the sign of the derivative and how the sign changes...then look for similar slope changes in the matching f(x) graph.

Reminder Trick to avoid confusion:

 Concentrate only on +ve or -ve part   derivative graph .The zero crossing in the f '- graph is the '0' slope point of the f-graph.If you remember this you can identify the related graphs...with some additional checks.

The positive part between two zeros in the f '-graph is the positive slope of the f-graph and vice versa.

You can easily be carried away in a maze when you start analyzing derivative as increasing decreasing slopes-so avoid looking at it the f ' graph (it is mental trick to avoid confusion) though you will be tempted by habit.

More exercises on increasing decreasing

Derivative graphic Tester1(geogebra) Tester2(desmos)

day 11

Derivatives 2

The slide show has some videos to be seen in links in slide 4

Day 10

Limits of trigonometric functions (no proof for now -only memorise)

The property is derived from squeeze theorem (because substitution produces 0/0) Sq Theorem Video Khan

Results

Lim x =>0    ( sin x)/x  =1

Lim x=>0     (1-cos x)/x  = 0

Lim x=>0    (tan x)/x = 1

TIP:  Squeeze theorem  is a useful tool for solving.However you should develop the skill to identify problems (in limits only) where it can be applied.I noticed that when you are given a function (mainly combined with trigonometric) , where   limits of a part of the function are known,then the problem can be manipulated algebraically (by addition,subn, multpln, divn,exp ) and fitted to suit the application of the theorem and limits derived for the function.The blog will not deal with it as it can be done at school...however remember the above limits.

----------------------------------------------------------------------------------------------------------------------------------

We shall be doing problems in derivatives after completing the intro in slides.
Visual Intro to derivatives-slide show