QUESTIONS:
2014; 1a
2013; 1a
2012; 1a
DIFFERENTIATION
f(x)= ax n
The process that gives the
gradient function/derivative of
a function
The function can be written as f(x), y,
The corresponding gradient function can be written as
f’(x), dy
dx
When a term is written as x it is important to remeber
that it is actually x1 therfore the derivative of f(x)=x is
f’(x)= x1 f’(x)= 1x1-1 f’(x)= 1x0 f’(x)= 1.1 f’(x)= 1
The derivtive of a number (constant) without an x is
always 0, f(x)= 2
f’(x)= 0
f’(x)= nax n-1
for instance y= 10x
-2
f(t)= t - 3t
2 4
2
or
Simple questions will require you to just
differentiate a simple term
Higher level questions will require you to
diferentiate complex terms or use the derivative in another formula once it has been
found
practice Question
Solve y= 10x
-2
f(t)= t - 3t
2 4
2
or
Example One
Example Two
Differentiate the
function to find the
derivative
Differentiate the
function to find the
derivative
Function
dy
= 10x-2-1
dx
dy
dy
Differentiate
= 10x-2-1
= -2.10x-2-1
dx
dx
function
dy
= -20x-3
dx
dy
And get dx = -20x-3
Function
t - 3t
f’(t)= 2
4
1-1
Derivative form
t - 3t
f’(t)= 2
4
1-1
Differentiate
function
2-1
Derivative form
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f(t)= t - 3t
2 4
2
y= 10x -2
-2-1=-3
2-1
2-1=1
1
0
f’(t)= 2t - 3t
2 4
1-1=0
2-1
- 1.3t 1-1
f’(t)= 2.t
2
4
=1
f’(t)= t - 3
4
And get f’(t)= t - 3
4