2. d
1. dx ( c ) = 0 ( c is a constant )
Ex f ( x) = 5
. f ′( x) = 0
2.
d n
dx
( )
x = nx n −1 ( n is a real number )
Ex f ( x) = x 7
.
f ′( x) = 7 x 6

3. d d
3. dx ( cf ( x) ) = c dx ( f ( x) ) ( c is a constant )
8
Ex f ( x) = 3 x
( )
. f ′( x) = 3 8 x 7 = 24 x 7
d d d
4. dx  f ( x ) ± g ( x )  = dx [ f ( x)] ± dx [ g ( x) ]
 
Ex f ( x) = 7 + x12
. f ′( x) = 0 + 12 x11 = 12 x11

4. f ( x) = 5x3 − 2 x 2 + 7 x + 4

5. f ( x ) = 3 x 2 − 4 x −3 + 1

6. f ( x) = 6x2 + 6
x = −2

7. y = 4 x3 + 2 x
dy
f ' ( x) =
dx
d2y
f "( x) = 2
dx

8. 4
f ( x ) = 10 x − 2 + 2
x

9. f ( x) = 6 x 2 − 5x + 2
f ( x ) = 4 x 3 + 10 x − 7
2 3 9 2
f ( x) = x + x + 3
3 2
3
f ( x ) = −3 x + 5 x − 3x +
7 4 2
5

10. f ( x ) = 2 x + 3x + 1
3
1 6 2
f ( x) = x + − 2
3 x
4 2
f ( x) = 2 + x
x 5
f ( x ) = 100 − 6 x − 3x 4

11. f ( x) = x7 + x5
y = x2 + 4x + 3
D( t ) = 40t − 10t 2
y = 4x +1

12. f ( x ) = 3x 3 + 2 x
f ( x) = x 4 + x3
3
H ( x ) = 2 + 3x 2
x
g ( x) = x + x
−1 −2