Найти производную функции f(x)=x^2/2x-1

Question

Найти производную функции f(x)=x^2/2x-1

Answer 1

f(x)' = (x^2/2x-1)' = ( (x^2)' (2x-1) -x^2*(2x-1)' ) / (2x-1)^2 =

= ( 2x (2x-1) - x^2*2 ) / (2x-1)^2 = ( 4x^2 -2x - 2 x^2 ) / (2x-1)^2 =

= ( 2x^2 -2x ) / (2x-1)^2 = 2x( x -1 ) / (2x-1)^2