Page 75 - Past Year

73 | P a g e

dy
y
15. Find for 2x y y 2 2  2e by using implicit differentiation.
dx

16. (a) Find the slope of a curve y  5x  2 3 at the point x  by using the first principle
2

of differentiation.
2
2
x d y dy
(b) If y  Ax  2 Bx , show that  x  y  0 .
2 dx 2 dx

17. Differentiate the following with respect to . Give your answer in the simplest form.
xe 3x
3
x
(a) f ( )  (b) ( )f x  (3x  2)(x  4)
x  3
18. Find '(2)f for ( ) 2f x  x  2 x by using the first principle.

19. Differentiate the following with respect to x. Give your answer in the simplest form.

4
(a) f ( )   x  9 x   2
x
2x   4 3
x
(b) f ( ) 
x  3
 
3

x
(c) f ( ) ln 2x    3 e 3x
dy
3
2

4y
2
20. (a) Find for y  2x y xe  by using implicit differentiation.
dx
dy
0
Hence, evaluate at y  .
dx
2
(b) Prove that if y   Ax B e   2x then d y  4 dy  4y  .
0
dx 2 dx
dy

2
21. Find for y  3x y  7xy  1 0 by using implicit differentiation. Hence, determine all
2
2
dx
dy
values of when y  1.
dx
22. Differentiate the following with respect to x. Give your answer in the simplest form.
(a) y   x  2  3 e (b) y  ln   x  1   3
5x
 5x   2 2
2
f
' f
x
23. Find   x for   x   2x   1 by using the first principle. Hence, find   2f ' .