Solving for a variable in the partial derivative of a summation

In summary, solving for a variable in the partial derivative of a summation is important for finding the rate of change of a function with respect to that variable. To solve for the variable, you need to take the partial derivative, set it equal to zero, and solve algebraically. The difference between a partial derivative and a regular derivative is that the former holds all other variables constant. The chain rule may need to be applied multiple times in this context. Some practical applications include optimization, modeling, and determining efficiency in various fields such as economics, physics, and engineering.
  • #1
bpk356
2
0
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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  • #2
Here's the partial derivative:
[tex][/tex]
[tex][/tex]

I can't get the LaTeX right...
 
Last edited:

1. What is the purpose of solving for a variable in the partial derivative of a summation?

The purpose of solving for a variable in the partial derivative of a summation is to find the rate of change of a function with respect to that variable. This is important in many scientific and mathematical applications, such as optimization and modeling.

2. How do you solve for a variable in the partial derivative of a summation?

To solve for a variable in the partial derivative of a summation, you need to first take the partial derivative of the function with respect to that variable. Then, you can set the resulting equation equal to zero and solve for the variable algebraically.

3. What is the difference between a partial derivative and a regular derivative?

A partial derivative measures the rate of change of a function with respect to one variable while holding all other variables constant. In contrast, a regular derivative measures the rate of change of a function with respect to one variable without considering other variables.

4. Can you explain the chain rule in the context of solving for a variable in the partial derivative of a summation?

The chain rule is a rule for finding the derivative of a composite function. In the context of solving for a variable in the partial derivative of a summation, this means that you may need to apply the chain rule multiple times if the variable you are solving for appears in multiple functions within the summation.

5. What are some practical applications of solving for a variable in the partial derivative of a summation?

Solving for a variable in the partial derivative of a summation has many practical applications, such as in economics, physics, and engineering. For example, it can be used to optimize production processes, model population growth, and determine the maximum efficiency of a system.

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