the function

Question

let f(x)=1/x.

Find f ⁱ (x), f ⁱⁱ (x), f ⁱⁱⁱ (x) and f⁽⁴⁾(x).

Deduce f ⁽ⁿ⁾ (x).

 

Answer 1

f(x) = x^(-1)

 

f'(x) = (-1)x^(-2)

 

f''(x) = 2x^(-3)

 

f'''(x) = (-6)x^(-4)

 

f''''(x) = 24x^(-5)

 

 

 The nth derivative is  (-1)^n*n! * x^[(-1)*(n+1)]