C(t) =
[tex]2.001 \times \frac{1}{1 + 2000e {}^{ - 2.4t} } [/tex]
( 1 / v ) ' = - v ' / v² et ( e^u ) ' = u ' e^u
[tex]v(t) = 1 + 2000e {}^{ - 2.4t} [/tex]
v'(t) =
[tex]2000 \times ( - 2.4)e {}^{ - 2.4t} = - 4800e {}^{ - 2.4t} [/tex]
C ' (t) =
[tex]2.001 \times - \frac{ - 4800e {}^{ - 2.4t} }{(1 + 2000e {}^{ - 2.4t}) {}^{2} } = [/tex]
