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from __future__ import division
from sympy import *
init_session(quiet=True)


    

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T,delta,rho_r,b_m,c_m,a_m,R_u = symbols('T,delta,rho_r,b_m,c_m,a_m,R_u')
W = symbols('W', cls=Function)(delta)

alphar = -log(1-delta*rho_r*(b_m-c_m)) - sqrt(2)*a_m/(4*R_u*T*b_m)*log(W);
display(alphar)
for ndelta in range(1,5):
    ss = simplify(diff(alphar, delta, ndelta))
    display(ss)

W =(1+delta*rho_r*(b_m*(1+sqrt(2)+c_m))) / (1+delta*rho_r*(b_m*(1-sqrt(2)+c_m)))
for ndelta in range(1,5):
    display(diff(W,delta,ndelta))


    

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