Ex. No. 4.1
1.
Find the rate of change of demand (x) of a commodity with respect to its price
(y) , if.
i. (i) y = 15 + 17x + 35x2 [video]
ii. y = 48x + log(x+3) [video]
iii. y = 5 + x2e-x + 2x [video]
iv. y = (3x+7)/(2x2+5) [video]
2.
Find the marginal demand of a commodity where demand is x and price is y.
(i) y = (5x+7)/2x-13)
[video]
(ii) y = e/e^x + xlogx.
[video]
3.
Differentiate the following function in their appropriate domains with respect
to x:
(i) y=cos^1sqrtx [video]
(ii) y=cot^
12x^3+1 [video]
(iii) y =
cosec^-1x / x^2+1
(iv) y = 2^sin^-1x
(v) y =
cos^-1(sin5x)
(vi) y = tan
^-1 (cot2x)
(vii) y =
cos(sec^-13/x)
(viii) y = cos^-1 (1-2sin^2x)
[video]
4. Find dy/dx for the following:
ii. y = sin ^ -1 (8x / 1 + 16x^2 ) [video]
iii. y = cos ^ -1 (1 - 25x^2 / 1+ 25x^2 ) [video]
iv. y = tan ^ -1 (6x / 1 - 5x^2 ) [video]
v. y = cot ^ -1 ( 1+ 12x^2 / x) [video]
vi. y = tan ^ - 1 ( 2 - 5x / 5 + 2x) [video]
vii. y = tan ^ - 1 ( 5- 4x / 1 + 20x) [video]
viii. y = cosec ^ -1 ( 1/ 2x^2 - 1)
[video]
