DIFFERENTIATION

1. 
   

   [ ( √ (^) √ √ )] is
   equal to:
   (a) (^) √ (^ ) (^) √ (b)
   √ (^2) √ √ ( ) 3
   (c) √ √ (^ ) (d) √ ( )( )

   
   


2. 
   

   If x= a Ѳ, y= a Ѳ, then^ at

   
   

Ѳ=^ is:

(a) -1 (b) 1 (c) - (d)

3. For | | , let y= 1+x+ +...... to ,

then^ equals to:

(a)^ (b)^
(c)
(d) x^

(^)

4. If x+ y=^ , then^ is equal

to:

(a)^ (b) - (c)^ (d) -

5. If y=
   (^ ), then^ is equal to:

(a)^ (b) (c) sec x tan x (d)

(^ )

6. If sin y= x sin (a+y), then^ is:

(a) sin (a+y) (b) (a+y) (c)^

(^) ( )
(d)^ (^ )
7. If y= (^).^ /, then
(a) 2 (b) -1 (c)^ (d)^

8. If f(x)= sin (cos x), then f ‘(x) is:
   (a) cos (cos x) (b) sin (- sin x) (c) – sin

(cos x)

(d) – sin x cos (cos x)

9. 
   

   If y= (^) √√ + √√^ , then
   is equal to:^
   (a) (^
   √^ )^
   (b) (^
   √^ )^
   (c) (d) 0

   
   


10. 
    

    If y= √ √ (^) √ .......,
    then^ is equal to:
    (a) (b) (c)^
    (d)

    
    


11. 
    

    If x= 3 cos Ѳ – 2 Ѳ, y= 3 sin Ѳ –
    2 Ѳ, then^ is:
    (a) cot Ѳ (b) tan Ѳ (c) sec Ѳ (d) cosec
    Ѳ

    
    


12. 
    

    If ( )^ = , then what is
    the value of^?
    (a)^ (b) xy (c)^ (d) 1

    
    


13. 
    

    What is the derivative of x?
    (a)^ (b) 0 (c) (d)^

    
    


14. 
    

    What is the derivative of
    | | | | at x=3?
    (a) – 3 (b) 3 (c) 0 (d) 2

    
    


15. 
    

    What is the derivative of?
    (a) 2 sec x (sec x + tan x) (b) 2
    ( )^ (c) 2
    ( )^ (d) sec
    x( )^