Question

với g(x)=\(\frac{x^2-2x+5}{x-1}\); g'(2) bằng:

Answer 1

g(2)=\(\frac{2^2-2\cdot2+5}{2-1}=5\)

Answer 2

g'(x)= \(\frac{\left(x^2-2x+5\right)'\left(x-1\right)-\left(x-1\right)'\left(x^2-2x+5\right)}{\left(x-1\right)^2}\)

       = \(\frac{\left(2x-2\right)\left(x-1\right)-\left(x^2-2x+5\right)}{\left(x-1\right)^2}\)

        = \(\frac{x^2-2x-3}{\left(x-1\right)^2}\)

   g(2) = \(\frac{2^2-2.2-3}{\left(2-1\right)^2}\)=-3