Partial derivative of Vxx w.r.t. r in terms of Vxx

Thread starter mramzan476
Start date Aug 10, 2020
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Derivative Partial Partial derivative Terms

In summary, a partial derivative is a mathematical concept used in multivariable calculus to describe the rate of change of a function with respect to one of its variables while holding the other variables constant. "Vxx" represents the second derivative of the function V with respect to the variable x, and the partial derivative of Vxx w.r.t. r is important because it allows us to understand the function's change with respect to r while keeping other variables constant. This can be calculated using the chain rule or the definition of a partial derivative. Taking a partial derivative in terms of Vxx allows us to isolate the effect of this variable on the function and make predictions based on changes in this variable.

Aug 10, 2020

mramzan476

Can anyone please help me to write partial derivative of Vxx w.r.t. r in terms of Vxx as shown in the hand written box at the end.

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Aug 10, 2020

PeroK

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Perhaps this is more mathematics than Earth Science!

Aug 10, 2020

mramzan476

Dear sir Perok, I do agree with you but Equation (10) is actually related to Earth Science/geo-physics.

1. What is a partial derivative?

A partial derivative is a mathematical concept that measures the rate of change of a function with respect to one of its variables, while holding all other variables constant.

2. What is Vxx?

Vxx is a mathematical notation used to represent the second partial derivative of a function with respect to the variable x. It is also known as the second order derivative of the function.

3. What does it mean to take a partial derivative of Vxx with respect to r?

Taking the partial derivative of Vxx with respect to r means finding the rate of change of the second partial derivative of a function with respect to the variable x, while holding the variable r constant.

4. How is the partial derivative of Vxx w.r.t. r calculated?

The partial derivative of Vxx with respect to r is calculated by taking the second partial derivative of the function with respect to x, and then substituting the variable r for x in the resulting expression.

5. What is the significance of calculating the partial derivative of Vxx w.r.t. r in terms of Vxx?

Calculating the partial derivative of Vxx with respect to r in terms of Vxx allows us to understand the relationship between the second partial derivative of a function with respect to x, and the variable r. It also helps in solving problems related to optimization and finding critical points of a function.