Question

Найти производную

y = (корень(1- x^2)) /x

Answer 1

$y'= frac{( sqrt{1-x^2} )'*(1-x^2)'x-( sqrt{1-x^2} )x'}{x^2}= \ \ = frac{ frac{1}{2 sqrt{1-x^2} }*(-2x)*x- sqrt{1-x^2} }{x^2}= \ \ = frac{ frac{-x^2-( sqrt{1-x^2} )^2}{ sqrt{1-x^2} } }{x^2}= frac{-x^2-1+x^2}{x^2 sqrt{1-x^2} }=- frac{1}{x^2 sqrt{1-x^2} }$