In [1]: from sympy import symbols, log, diff
In [2]: a,b,c,v,t = symbols("a b c v t",real=True)
In [3]: u=a*log((b/a)*t+1)+c+v*t
In [4]: print(diff(u,t))
b/(1 + b*t/a) + v
In [1]: from sympy import symbols, log, diff
In [2]: a,b,c,v,t = symbols("a b c v t",real=True)
In [3]: u=a*log((b/a)*t+1)+c+v*t
In [4]: print(diff(u,t))
b/(1 + b*t/a) + v