Question

how do you find the derivative of f(x)=2x/(x^2+x+1)^1/2 HELP A.S.A.P.?

Answer 1

carefully use the quotient rule

f'(x) = [ (x^2+x+1)^(1/2) (2) - (1/2)(x^2 + x + 1)^(-1/2) (2x+1)(2x) ]/(x^2 + x + 1)
= [ (x^2+x+1)^(1/2) (2) - (x^2 + x + 1)^(-1/2) (2x+1)(x) ]/(x^2 + x + 1)
= (x^2+x+1)^(-1/2) [ 2(x^2+x+1) - x(2x+1) ] / (x^2+x+1)
= (x+2)/(x^2+x+1)^(3/2)