DIFFERENTIATION
1. Derivative by first principal
2. Finding gradient of function at any point (X,Y)
𝑑𝑦
 Find
𝑑𝑥
 Put X in

𝑑𝑦
𝑑𝑥
>0
𝑑𝑦
𝑑𝑥
increasing curve

𝑑𝑦
𝑑𝑥
<0
decreasing curve
3. Basic formula and general rules for differentiation
4. Product rule
5. Quotient rule
6. Composite function differentiation
7. Finding equation of a tangent at given point (X,Y)
 Find gradient (m) at given point (X,Y)
 Use slope point form to get the tangent equation
8. Finding equation of a normal at given point (X,Y)
(Normal=perpendicular to tangent)
 Find gradient (m) at given point (X,Y)
 Find gradient of perpendicular line by using
 Use slope point form to get the tangent equation
9. Use of second order derivative
(tells us about concavity)
10.
>0
opening up
<0
opening down
Finding local maxima or minima
condition
𝑑𝑦
 =0

𝑑𝑥
𝑑𝑦
𝑑𝑥
should change the sign left or right to the point
 Find
𝑑𝑦
𝑑𝑥
equate it to zero
 Use sign diagram to check that derivative changes
sign left or right to point
11.
Finding maxima and minima using second
derivative
 Find
𝑑𝑦
𝑑𝑥
=0

should change concavity

>0
minima

<0
maxima
12.
Find inflection point using second derivative

=0

Changes sign left to right of that point
13.
Optimizing the quantity using differential calculus
 Get an equation for optimization
𝑑𝑦
 Find point where =0
𝑑𝑥
 Check whether its maxima or minima