Question

найдите производную функции f(x)=1/x+1/x^2 если f`(x)=3 f`(x)=1​

Answer 1

Ответ:

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

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

$f'(3) = - \frac{1}{9} - \frac{2}{27} = \frac{ - 3 - 2}{27} = - \frac{5}{27}$

$f'(1) = - 1 - \frac{2}{1} = - 3$