Question

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

Answer 1

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