Solving for a variable in the partial derivative of a summation

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SUMMARY

The discussion focuses on calculating the partial derivative of the function Q with respect to the variable w0, specifically in the context of a summation involving logistic regression. The original equation is Q(w_{0},w_{1},w_{2},w_{3}) = ∑(y_{i} - w_{2} * (1/(1 + e^{x_{i}w_{0} + w_{1}})) - w_{3})². The user successfully computes the partial derivative but struggles to isolate w0 after setting the derivative equal to zero. This indicates a need for further algebraic manipulation techniques to solve for w0.

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I'm trying to find the partial derivative of Q with respect to w0 and then set it equal to 0 and solve for w0. Finding the partial derivative was easy, but once I've got it, I'm having a hard time getting w0 by itself. Here's the original equation:

[tex] Q(w_{0},w_{1},w_{2},w_{3})=\sum\left(y_{i} - w_{2}\frac{1}{1+e^{x_{i}w_{0}+w_{1}}} - w_{3}\right)^{2}[/tex]
 
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Here's the partial derivative:
[tex][/tex]
[tex][/tex]

I can't get the LaTeX right...
 
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