4. Lesson Objectives
To Understand the application of Differentiation in
finding the gradient of a curve.
To understand the rules of Differentiation.
5. Pair Work
Research ( 5 Minutes)
RATE OF CHANGE
Gradient of curve
Relationship between rate rate of
change and gradient of curve
11. Lesson Objectives
To Understand the application of Differentiation in
finding the gradient of a curve.
To understand the rules of Differentiation.
12. DIFFERENTIATION
▪ It is the algebraic process used to find the gradient
function of any given function.
▪ The gradient function is called the Derivative.
13. Notation
The most common notations are:
The derivative of a function f(x) with respect to x is defined as f’(x).
Leibnitz notation used for f’(x) is dy
dx
14. f(x) f ′ (x)
x2
x3
x4
x5
xn
Spot the pattern
f(x) f ′ (x)
x2
x3
x4
x5
xn
f(x) f ′ (x)
x2
x3
x4
x5
xn
2x
3x2
4x3
5x4
nxn-1
THINKER
15. Rule of thumb:
▪ Multiply by the power and reduce the power by 1.
16. f(x) f ′ (x)
2x2
3x2
4x2
5x2
ax2
Spot the pattern
f(x) f ′ (x)
2x2
3x2
4x2
5x2
ax2
f(x) f ′ (x)
2x2
3x2
4x2
5x2
ax2
4x
6x
8x
10x
2ax
THINKER
17. Rules for differentiation
There are 4 rules for differentiating – remember these and you
can differentiate anything …
Rule Examples
1. f(x) = x6 f ′ (x) =
2.
f(x)= 4x3 f ′ (x) =
3. f(x) = 65 f ′ (x) =
f(x) = g(x) + h(x)
f ′ (x) = g′ (x) + h′ (x)
f(x)= x6 + 4x2 + 65 f ′ (x) =
6 x 6 - 1 = 6 x 5
4 x 3 x 3-1
= 12 x 2 or 12 x 2
0
6 x 5 + 8x
