Bonjour,
a)
[tex]f(x) = e^{-2x} + e^2[/tex]
[tex]f'(x) = -2e^{-2x}[/tex]
b)
[tex]f(x) = \frac{e^x}{x^2 + 3}[/tex]
[tex]u(x) = e^x[/tex] [tex]v(x) = x^2 + 3[/tex]
[tex]u'(x) = e^x[/tex] [tex]v'(x) = 2x[/tex]
[tex]f'(x) = \frac{u'v - uv'}{v^2} = \frac{e^x \times (x^2 + 3) - e^x \times 2x}{(x^2 + 3)^2} = \frac{x^2e^x + 3e^x - 2xe^x}{(x^2 + 3)^2} = \frac{e^x(x^2 + 3 -2x)}{(x^2 + 3)^2}[/tex]
