Partial Derivative of z=[x^2 tan^-1(y/x)]-[y^2 tan^-1(x/y)] with Respect to y

In summary, partial differentiation is a mathematical concept used in calculus to calculate the rate of change of a function with respect to one of its several independent variables while holding the other variables constant. It is different from ordinary differentiation in that it allows us to analyze the impact of each variable on the function separately. Partial differentiation is used in various fields, particularly in analyzing functions with multiple variables. The notation for partial differentiation involves using subscripts to indicate which variable is being held constant. Its purpose is to understand the relationships between variables in complex systems and to solve equations with multiple variables.
  • #1
avinash patha
5
0
given that z=[x^2 tan^-1(y/x)]-[y^2 tan^-1(x/y)].find value of [z][xy].
where [z][xy] stand for partial derivative w.r.ty(partial derivative of z w.r.tx)
 
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  • #2
That's not really a question, is it? Just start taking the derivatives. Use the product and chain rules. You can make life a little easier by noticing the two terms are related by an interchange of x<->y. So you could just do one and use that to figure out what the other one is.
 

1. What is partial differentiation?

Partial differentiation is a mathematical concept used in calculus to calculate the rate of change of a function with respect to one of its several independent variables while holding the other variables constant. It is a way to analyze the impact of one variable on a multivariable function.

2. How is partial differentiation different from ordinary differentiation?

Ordinary differentiation involves finding the rate of change of a function with respect to a single independent variable. In partial differentiation, we are finding the rate of change of a function with respect to one independent variable while keeping the others constant. This allows us to analyze the impact of each variable on the function separately.

3. When is partial differentiation used?

Partial differentiation is used in many fields of science and engineering, including physics, economics, and engineering. It is particularly useful in analyzing functions with multiple variables, such as in optimization problems and in the study of multivariable systems.

4. What is the notation for partial differentiation?

The notation for partial differentiation involves using subscripts to indicate which variable is being held constant. For example, the partial derivative of a function f with respect to the variable x would be written as ∂f/∂x. If there are multiple variables, the notation would be ∂f/∂xi, where i represents the subscript for the variable being held constant.

5. What is the purpose of using partial differentiation?

Partial differentiation allows us to understand how a multivariable function changes with respect to each of its independent variables. This is helpful in optimizing functions and understanding the relationships between variables in complex systems. It also allows us to solve equations with multiple variables by treating them as separate entities.

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