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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 $f_{1}(c,p) = \dfrac{1}{2}r_{c}c^{2}+\dfrac{1}{4}u_{c}c^{4}+\dfrac{1}{6}v_{c}c^{6}+\dfrac{1}{2}r_{p}p^{2}-\gamma cp-Ep$
Step1:  $\dfrac{\partial f_{1}(c,p)}{\partial p} = 0 = $
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Python Code:
f1 = (1/2)*r_c*c**2+(1/4)*u_c*c**4+(1/6)*v_c*c**6-E*p+(1/2)*r_p*p**2-gamma*c*p
Explanation: $f_{1}(c,p) = \dfrac{1}{2}r_{c}c^{2}+\dfrac{1}{4}u_{c}c^{4}+\dfrac{1}{6}v_{c}c^{6}+\dfrac{1}{2}r_{p}p^{2}-\gamma cp-Ep$
End of explanation
pmin = solve(f1.diff(c),p)[0]
pmin
E_cp = solve(f1.diff(p),E)[0]
E_cp
expand(E_cp.subs(p,pmin))
Explanation: $\dfrac{\partial f_{1}(c,p)}{\partial p} = 0 = $
End of explanation
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