EXERCISES ON DIFFERENTIATION AND APPLICATIONS OF DIFFERENTIATION _._..._. _._.._._._.._._._._._._._..._._...._._._-.._._._._._._-._._._.._.._.. 1. Find from the rst principles the derivatives of the following functions , _ 1 L f(I)~ (1,___1)2 ii. at) = \\/:r+1 iii. x) = 4213: iv. f(x) = sin(3:r) 2. Differentiate the following functions with respect to :r. _12+4I+3 _V'E'1 "' f(x)\"'/E+1 3. Find the derivative of each of the following functions: i. f(:r) = tan(3:r:) 4sec(5:i:) ,, _ ein2(:r) 11. at) cos(:r) iii. f(:t:) = V1 + 2tan(:r:) iv. ue) = sin3(:r) + cos3(:r) v. x) = sec2(2:c) tan2(2x) _ _ ein(:r) + cos(:r) v1. at) _ 5in(:.':) cos(:r) 4. If F(:r) = f(g(:r)) and 9(3) = 6. g'(3) = 4, f'(3) = 2 and f'(6) = 7, nd F'(3)