Bonjour,
[tex]f(x) = \frac{2x + 1}{x-3}[/tex]
u(x) = 2x + 1
u'(x) = 2
v(x) = x - 3
v'(x) = 1
[tex]f'(x) = \frac{u'v - uv'}{v^2} = \frac{2 \times (x-3) - (2x +1) \times 1}{(x - 3)^2} = \frac{2x -6 -2x -1}{(x - 3)^2} = \frac{-7}{(x - 3)^2}[/tex]
[tex]g(x) = \frac{6x^2 -2x +1}{x}[/tex]
u(x) = 6x² -2x + 1
u'(x) = 12x - 2
v(x) = x
v'(x) = 1
[tex]g'(x) = \frac{(12x - 2) \times x - (6x^2 - 2x + 1) \times 1}{x^2} = \frac{12x^2 -2x -6x^2 + 2x -1}{x^2} = \frac{6x^2 -1}{x^2}[/tex]
