Ex. No. 4.1

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 [video]

 

(iv) y = 2^sin^-1x [video]

 

(v) y = cos^-1(sin5x) [video]

 

(vi) y = tan ^-1 (cot2x) [video]

 

(vii) y = cos(sec^-13/x) [video]

 

(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]