Hi

f(t) = 5000 e^(u(t)) where u(t) = 0.1 e^(0.25 t)

f'(t) = 5000 u'(t) e^(u(t))

Now we need to calculate u'(t)

u(t) = 0.1 e^(v(t)) where v(t) = 0.25 t

u'(t) = 0.1 v'(t) e^(v(t)) = 0.1 x 0.25 e^(v(t)) = 0.025 e^(0.25 t)

f'(t) = 5000 x 0.025 e^(0.25 t) e^(0.1 e^(0.25 t)) = 125 e^(0.25 t) e^(0.1 e^(0.25 t))