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x
e  e  x  dy  2
8. If y  , show that    y  2 1.
2  dx 
2
B 2 d y dy
9. Given y  Ax   2ln x, show that x  x  y  2ln x .
x dx 2 dx

10. Differentiate the following with respect to x .
3x  1 3

(a) y  (b) y  2x   3 ln 4x   5 .
x  2

dy dy


2
2
11. (a) Find if x  3y  2xy  19 0. Hence, evaluate at 2,3 .
dx dx
3
(b) Given y   Ax B e  x , find the constants A and B if y  and dy  5 when
dx
x  0 .

2
12. Find '( )f x for ( ) 3f x  x  2x  1 by using the first principle.

dy

13. (a) Find for e 4x (x y  2 1) 1.
dx
ln(x  1) dy 1  1 ln(x  1) 
(b) Given y  , show that    
x dx x  x  1 2x 

14. Differentiate the following with respect to x :

2 2
x
(a) f ( )   3x  x
3
3x 3
(b) ( )f x    2x   1   x  2  1
 x 

2 x 
(c) ( ) ln(f x  x e 2 5x  1 )