Page 25 - (1-1)eng

(1 - 1) The First Derivative of a Function – G(B)
Group (B)

Complete each the following
S.B. 11) If f , g , q are three differentiable functions x 1 2
 ( x ) – 1 4
with respect to x , complete each of the g ( x ) 2 1
following using the values given in the ' ( x ) 1 5
g' ( x ) 2 – 3
opposite table

(a) If q ( x ) = 3  ( x ) – 2 g ( x ) , then q' ( 1 ) = … … …
(b) If q ( x ) =  ( x ) [ 5 + g ( x ) ], then q' ( 2 ) = … … …
(c) If q ( x ) =  ( x )  [ g ( x ) + 2 ] , then q' ( 1 ) = … … …

(d) If q ( x ) =  ( g ( x ) ) , then q' ( 1 ) = … … …

x
g
(e) If q ( x ) = 3x     , then q' ( 2 ) = … … …
 
(f) If q ( x ) = x   3  g x   2 , then q' ( 1 ) = … … …
dx 1 dy
12) If x + y = 3 , and = , then = … … …
dt 2 dt
n
2
3
13) If ƒ ( x ) = x + x + x + . . . + x then ƒ' ( 1 ) = … … …
S.B. 14) Put (  ) or (  )
t t  t 1  2
The rate of change of t 2 3 with respect to is ( )
t 1 t 2 3

Answer the following questions

3
5
2 2003 15) If x = ( y – 1 ) , prove that dy  y 3 1 .
nd
dx 15 x y 2

16) If y = 2 x and z  1 x 2 , show that dy   2  dz .

1 x 2 x dx z 2 dx
1 3  dy  2 2
17) If y = x + , prove that 4 x   = ( x – 1 ) .
x  dx 
dz  dy 
2
2
4 1 
3
18) If y = 2 x  , z = ( 1 – 2 x ) , then prove that   y  = 0.
dx  dx 
dy dx 5
3
2
st
1 1996 19) If y = x – 5 x + 4, x = z – 1, prove that + 7 – 6 z = 0.
dz dz
2
20) If y = z , z = 1 – L , L = 2 x, prove that y dy + 2 L = 0.
dx
x  1 dy
2
21) If y = x + x, z = , find at x = 1. [ 6 ]
x dz
2 d 
S.B. 22) If  ( x ) = and g ( x ) = 3 x, find [ (   g ) ( x ) ] at x = – 2.   6  
x  1 dx  25 
Calculus 24 Unit (1)