Page 76 - Past Year

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' f
24. Find   x for   3f x  x  2 2 by using the first principle. Hence, or otherwise, find the
value of   x at x  1.
' f
25. Given y  Ae  x ln x , where A is a constant.
2
d y
2
0
(a) Show that x 2  yx  Ae  x 2x   1  .
dx 2
dy
(b) Find the value of A if  1 when x  1. Give your answer in exact value.
dx
26. Use suitable rules of differentiation to find the derivative of the following functions. Give
your answer in the simplest form.
(a)   x  x e
3 7x
f

(b)   x  h x ln x e ln x
dy 2
27. Apply implicit differentiation to find for the equation x y  xy  2. Hence, solve for
dx
dy
x when  0. Give your answer in exact value.
dx
2
2
3
28. Determine the values of A, B and C for y  Ax  B x   1  Cx , if dy  2and d y  1
dx dx 2
at the point (2, 1).

dy dy
2
2
29. If 4y  3x  5xy  , find in terms of and . Hence evaluate when = 0.
8
dx dx
x 3 dy Ax 2 x B 
30. (a) Given y  and  . Find the values of and .
 x   1 2 dx x   1 3

1 dy
(b) Given y  4x 3x  3  2 , find in the simplest form.
2
dx

2
2
31. (a) Given y  4 5x e   3x , find d y in the simplest form. Hence evaluate d y when
dx 2 dx 2
= 0.

dy
(b) Find in terms of x and y, given that    y ln x where > 0 and > 0.
ln 2y
dx
dy
Give your answer in the simplest form. Hence evaluate when = 1.
dx