Page 261 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes dv
differentiating v w.r.t. x, we get .
dx
dy dy du dv
. . which is chain rule.
dx du dv dx

Notes General Rules

d n n 1 d
x
x
1. f ( ) n f x f ( )
dx dx
d f ( ) f ( ) d
x
x
2. e e f ( ) x
dx dx
d 1 d
( )
3. log f x f x etc.
e
dx f ( ) x dx
Example: Differentiate the following functions w.r.t. x:
1. x 2 1

Solution: Let y x 2 1
dy 1 d 2
x 1
dx 2 x 2 1 dx

1
2x
2 x 2 1
x
x 2 1

2. ax 2 bx c 5

Solution: Let y ax 2 bx c 5

dy 5 1 d
5 ax 2 bx c ax 2 bx c
dx dx
5 ax 2 bx x 4 2ax b

3. e 2x 3
Solution: Let y e 2x 3

dy 2x 3 d
e 2x 3
dx dx
e 2x 3 (2)
2e 2x 3

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