Question

Найдите производную функции y(x)=1/корень из x^2+1

Answer 1

У(x) = 1/√(x²+1) ;
у'(x) = (1/√(x²+1) ) ' = ((x²+1)^(-1/2))  ' = (-1/2)*(x²+1)^(-3/2)*(x²+1)' =
(-1/2)*(x²+1)^(-3/2)*2x =  -x*(1/√(x²+1)³) = -x /√(x²+1)³. 
* * * или
у'(x) = (1/√(x²+1) ) ' = ( (1)'*√(x²+1) - 1*(√(x²+1))' )/(√(x²+1) )² =
(0 -(1/2)*(x²+1)^(-1/2)*(x²+1)' )/ (x²+1) = -x*(x²+1)^(-1/2) /(x²+1) =
- x *(1/(x²+1)^(1/2) ) / (x²+1) = -  x / (x²+1)√(x²+1)  -x /√(x²+1)³.

Answer 2

Y=(x²+1)∧(-1/2), y'=-1/2*(x²+1)^(-3/2)*2x=-x/√(x²+1)³