Question

Производные высших порядков: Найдите f(4)(x), если f(x) = - 3/x​

Answer 1

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