Question: A problem related to chain rule derivative

i have two expressions. S1 and S2 are functions of sigma and tau. but i need derivative of sigma and tau with respect to S1 and S2. what should i do ? could any one help?


 

restart

S1 := -4*sqrt(sigma1^2 + 4*tau^2)*tau^2/((sigma1 + sqrt(sigma1^2 + 4*tau^2))^2*(1 + 4*abs(tau/(sigma1 + sqrt(sigma1^2 + 4*tau^2)))^2))

-4*(sigma1^2+4*tau^2)^(1/2)*tau^2/((sigma1+(sigma1^2+4*tau^2)^(1/2))^2*(1+4*abs(tau/(sigma1+(sigma1^2+4*tau^2)^(1/2)))^2))

(1)

S2 := 4*sqrt(sigma1^2 + 4*tau^2)*tau^2/((-sigma1 + sqrt(sigma1^2 + 4*tau^2))^2*(1 + 4*abs(tau/(-sigma1 + sqrt(sigma1^2 + 4*tau^2)))^2))

4*(sigma1^2+4*tau^2)^(1/2)*tau^2/((-sigma1+(sigma1^2+4*tau^2)^(1/2))^2*(1+4*abs(tau/(-sigma1+(sigma1^2+4*tau^2)^(1/2)))^2))

(2)

 

 

 


 

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