Higher derivatives

We define the higher derivatives of a function as:

· f’’(a) = (f’(a))’

· f’’’(a) = (f’’(a))’

· f^IV(a) = (f’’’(a))’ ……..

 

Example:

 

Exercise: calculate:

a) f'''(1) if f(x) = 1/x

b) All the higher derivatives of f(x) = x³ - 2x

 

 

 

 

 

Solutions: a) f'''(1) = -6; b) f'(x) = 3x² - 2, f''(x) = 6x, f'''(x) = 6; f^IV(x) = f^V(x) = ...... = 0