- #1
littlesohi
- 5
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I need help with this one:
Find fxy in:
ln(x+y)/(xy) .. the ln applies to the whole problem.
Find fxy in:
ln(x+y)/(xy) .. the ln applies to the whole problem.
Well.littlesohi said:I need help with this one:
Find fxy in:
ln(x+y)/(xy) .. the ln applies to the whole problem.
A partial derivative is a mathematical concept used to measure the rate of change of a function with respect to one of its variables, while holding all other variables constant.
To calculate a partial derivative, you take the derivative of the function with respect to the specific variable, treating all other variables as constants. This is done using the power rule, product rule, quotient rule, or chain rule, depending on the complexity of the function.
The partial derivative of ln(x+y)/xy with respect to x is 1/(x(x+y)), and the partial derivative with respect to y is 1/(y(x+y)).
Partial derivatives are important in many areas of mathematics and science, including economics, physics, engineering, and statistics. They allow us to analyze how a function changes in response to changes in specific variables, and are essential in optimization and gradient-based algorithms.
Partial derivatives are used in various real-life applications, such as determining the maximum profit for a company based on different variables, analyzing the relationships between different physical quantities in physics, and optimizing the performance of complex systems in engineering. They can also be used in data analysis and machine learning algorithms.