Page 109 - DECO403_MATHEMATICS_FOR_ECONOMISTS_ENGLISH

Mathematics for Economists

Note Again when x = 0
Then sin y 0 Ÿ y nS

2
S)
dy cos (an
At, x = 0 =
dx cosa
2
dy cos a
⇒ = =cos a
dx cosa
2
–1
2
–1
Example 9: If y = (sin x ) +(cos x ) , then prove that
2
2 dy dy
(1 – x ) – x = 4
dx 2 dx
1
1
Solution : y = (sin ) x 2 (cos x ) 2
1
1

dy 2(sin x cos x )
dx = 1 x 2
2 dy
1
1
⇒ 1 x = 2(sin x cos x )
dx
On differentiating with respect to x,
2
1 2 dy x ( 2 ). dy = 2 ª « 1 1 º »
x

dx 2 21 x 2 dx « 2 1 x 2 ¼ 1 » ¬
x
2
2 d y dy
(1 ) x x
dx 2 dx =2 . 2
1 x 2 1 x 2
2
2 dy dy
∴ (1 ) x x =4
dx 2 dx
Self Assessment
1. Multiple Choice Questions:
7
(i) What will be the differential coefficient of ax with respect to x ?
7
(a) C (b) x (c) x 7 (d) a 2
(ii) What will be the differential coefficient of log x with respect to tan x?
2
2
sin x cos x x x
(a) (b) (c) 2 (d) 2
x x cos x sin x
1
-1
(iii) Differential coefficient of tan x with respect to sin x at x = will be
-1
2
32 52 23 5
(a) (b) (c) (d)
5 3 5 23

102 LOVELY PROFESSIONAL UNIVERSITY