Question

Найдите производную функции F (x)=x-1/x и ее знасения при x= sqrt2
Плиз срочно!!!!

Answer 1

$f'(x)= (frac{x-1}{x} )'= frac{(x-1)'*x-(x-1)*x'}{ x^{2} } = frac{x-(x-1)}{ x^{2} } =frac{x-x+1}{ x^{2} } =frac{1}{ x^{2} }$
$f'( sqrt{2} )= frac{1}{ sqrt{2} ^{2} } = frac{1}{2}= 0,5$

Answer 2

y=(x-1)/x
y'=(x-(x-1))/x²=1/x²=1/(√2)²=1/2