Exercise 12.2

Find the derivative of x2 - 2 at x = 10.

Find the derivative of cos x from first principle.

Find the derivative of the following functions: (i) sin cosx x (ii) sec x (iii) 5sec 4cosx x+ (iv) cosec x (v) 3cot 5cosecx x+ (vi) 5sin 6cos 7x x− + (vii) 2 tan 7secx x−

Find the derivative of x at x = 1.

Find the derivative of 99x at x = l00.

Find the derivative of the following functions from first principle. (i) 3 27x − (ii) ( )( )1 2x x− − (iii) 2 / x (iv) 1 / x / x + −

For the function ( ) / 100 99 2 . . . 1100 99 2 x x xf x x= + + + + + . Prove that ( ) ( )1 100 0f f′ ′ = .

Find the derivative of 1 2 2 1. . .n n n n nx ax a x a x a− − −+ + + + + for some fixed real number a.

For some constants a and b, find the derivative of (i) ( ) ( )x a x b− − (ii) ( ) 22ax b+ (iii) x a x b − −

− − for some constant a.

Find the derivative of (i) 32 4x − (ii) ( ) ( )35 3 1 1x x x+ − − (iii) ( )3 5 3x x− + (iv) ( ) / 5 93 6x x −− (v) ( ) / 4 53 4x x− −− (vi) / 1 3 1 / x x x −+ −