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Re: Simple question: is it possible to take a derivative and solve for x ?

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  • Subject: [mg119322] Re: Simple question: is it possible to take a derivative and solve for x ?
  • From: David Skulsky <edskulsky at gmail.com>
  • Date: Mon, 30 May 2011 06:36:23 -0400 (EDT)

The derivative of the function you provided is very complicated and I'd be surprised if a symbolic solution to the equation is possible. Since you didn't provide any numerical values for the constants (l1, l2, v1, v2, c, L1, L2, V1, V2, C), there's not much Mathematica can do.

However, I have to wonder if you intended to have two sets of constants (lower-case and upper-case)? If not, then replacing the upper-case constants with the lower-case constants yields an answer:

In[156]:= f = ((x*l1 + (1 - x)*l2)/((x^2*v1 + (1 - x)^2*v2 + 2*x*(1 - x)*c)^0.5)) + ((x*
        L1 + (1 - x)*
        L2)/((x^2*V1 + (1 - x)^2*V2 + 2*x*(1 - x)*C)^0.5)) /. {L1 -> l1,
   L2 -> l2, V1 -> v1, V2 -> v2, C -> c}

Out[156]= (2 (l2 (1 - x) + l1 x))/(v2 (1 - x)^2 + 2 c (1 - x) x + v1 x^2)^0.5

In[157]:= Solve[D[%, x] == 0, x]

Out[157]= {{x -> (1. c l2 - 1. l1 v2)/(1. c l1 + 1. c l2 - 1. l2 v1 - 1. l1 v2)}}

David


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