Differentiate simple functions

Question

Q1) For f(x) = x^3 - x^-1

Find f'(x) , f''(x) and f'''(x)

 

Q2) Find the derivative of the following

a) y = sinx cosx

b) y = √x  cos x

c) y = (x + x^-2)sinx

 

Q3) Suppose that f(2) = 8 and f'(2) = -3. Use the product rule to find the derivative of  xf(x)  when x = 2

 

 

Answer 1

(1).

The function is f(x) = x³ - x ^{- 1}.

Answer 2

2.

Find the derivative of the following functions :

Answer 3

(3).

f(2) = 8 and f ^' (2) = - 3.