Question

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

Answer 1

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

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