Question

Найдите производную функции f(x) =(4+1/x²)³​

Answer 1

Ответ:

$f(x) = {(4 + \frac{1}{ {x}^{2}} )}^{3} = {(4 + {x}^{ - 2}) }^{3}$

$f'(x) = 3 {(4 + {x}^{ - 2}) }^{2} \times (4 + {x}^{ - 2} )' = \\ = 3 {(4 + \frac{1}{ {x}^{2}}) }^{2} \times ( - 2 {x}^{ - 3 } ) = \\ = - \frac{6}{ {x}^{3} } {(4 + \frac{1}{ {x}^{2} }) }^{2}$