The link @Stranger_On_A_Train gave is fine, but here’s a slightly different derivation of the Tsiolkovsky rocket equation:
Start with:
p=propellant flow rate (i.e., kg/s)
m0=initial mass
m1=final mass
Ve=propellant exit velocity
F=engine force
Then:
m(t) = m0 - p⋅t
And (since force is mass flow times exit velocity):
F=p⋅Ve
Since F=ma and a=F/m:
a(t) = p⋅Ve / (m0 - p⋅t)
We can integrate to:
v(t) = -Ve⋅ln(m0 - p⋅t) + C
The final time is (when the propellant is depleted):
t1=(m0 - m1)/p
Evaluating t from 0 to (m0 - m1)/p gives:
delta v = -Ve⋅ln(m0 - p⋅(m0 - m1)/p) - -Ve⋅ln(m0 - p⋅0) = -Ve⋅ln(m1) + Ve⋅ln(m0) = Ve⋅ln(m0/m1)
And that’s it. You can convert to a form using Isp by substituting Ve=Isp⋅g. Note that the flow rate drops out of the final formula.