Page 73 - Past Year

71 | P a g e

CHAPTER 8: DIFFERENTATION

dy
1. Find when x  for each of the following:
0
dx
 2  e 2x (2x  1)
3
(i) y  ln x  x  1 (ii) y  .
x  1

dy
2. Given ln y e xy , find
dx

2
d x e x
x

3. If y  x e , show that   0
dy 2  1 e x  3

dy
4. Find the value of at x  1 if
dx

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

2
2
4
5. Given that x  2xy  2y  . Solve for x and y if dy  0 .
dx

2
2
3
0
6. Let y  x  y  2x for x  .
(a) If y =1, find the value of x.
dy dy
(b) Find . Hence, evaluate when y = 1.
dx dx

B
7. Given y  Ax  2 , where A and B are constants and x  .
0
x
dy d y d y dy
2
2
0
(a) Find and . Hence, show that x 3  x 2  3B  .
dx dx 2 dx 2 dx
dy
(b) Find the values of A and B if y = 3 and  3 when x = 1.
dx