Question

Find the fourth derivative of f(x) = 3x^-1 ƒ(4) (x) =​

Answer 1

`f(x) = 3x^(-1)\\\\f'(x) = 3(-1) x^(-1-1) = -3x^(-2)\\\\f''(x) = -3(-2)x^(-2-1) = 6x^(-3)\\\\f'''(x) = 6(-3)x^(-3-1)=-18x^(-4)\\\\f''''(x) = -18(-4)x^(-4-1) = 72x^(-5)`

`\text{The fourth derivative of f(x) is}~ 72x^(-5).`