Spm-Add-Maths-Formula-List-Form4

Differentiation of a Function III
n
y = ax
dy
= anx
dx
n−1
Example
3
y = 2x
dy
= 2(3) x =
6x
dx
2 2
Differentiation of a Fractional Function
1
y = n
x
Rewrite
−n
y = x
dy −n−1 −n
=− nx =
dx x
Example
1
y =
x
−1
y = x
dy −2
−1
=− 1x
= 2
dx x
Law of Differentiation
n+
1
Sum and Difference Rule
y = u± v u and v are functions in x
dy du dv
= ±
dx dx dx
Example
3 2
y = 2x + 5x
dy
2 2
= 2(3) x + 5(2) x= 6x + 10x
dx
http://www.one-school.net/notes.html
10
Chain Rule
ONE-SCHOOL.NET
n
y = u u and v are functions in x
dy dy du
= ×
dx du dx
Example
2 5
y = (2x + 3)
2
du
u = 2x + 3, therefore = 4x
dx
5 dy 4
y = u , therefore = 5u
du
dy dy du
= ×
dx du dx
= ×
= 5(2x + 3) × 4x= 20 x(2x + 3)
4
5u 4x
2 4 2 4
Or differentiate directly
n
y = ( ax+ b)
dy
n−1
= na ..( ax+ b)
dx
2 5
y = (2x + 3)
dy
= 5(2x dx
+ 3) × 4x= 20 x(2x + 3)
2 4 2 4