Derivative in spherical coordinates

In summary, the conversation revolved around a problem statement and a partial solution involving the chain rule and partial derivatives in spherical coordinates. The individual expressed difficulty in finding the partial derivatives df/dt and d^2f/dt^2 and requested assistance. However, their attempts were not mentioned.
  • #1
williamcarter
153
4

Homework Statement


dmund.JPG
-here is the problem statement

dmund2.JPG
-here is a bit of their answer

Homework Equations


Chain rule, partial derivative in spherical coord.

The Attempt at a Solution


I tried dragging out the constant and partial derivate with respect to t but still I can't reach their df/dt and d^2f/dt^2 partial derivatives.
Any help would be much appreciated.
Thank you !
 
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  • #2
williamcarter said:

Homework Statement


View attachment 109867 -here is the problem statement

View attachment 109868 -here is a bit of their answer

Homework Equations


Chain rule, partial derivative in spherical coord.

The Attempt at a Solution


I tried dragging out the constant and partial derivate with respect to t but still I can't reach their df/dt and d^2f/dt^2 partial derivatives.
Any help would be much appreciated.
Thank you !
Please post your attempts anyway.
 

1. What is the definition of a derivative in spherical coordinates?

The derivative in spherical coordinates represents the rate of change of a function with respect to a change in one of the spherical coordinates (r, θ, φ).

2. How is the derivative calculated in spherical coordinates?

The derivative in spherical coordinates is calculated using the chain rule, where the partial derivatives with respect to each coordinate are multiplied by the corresponding unit vectors and added together.

3. What is the significance of the derivative in spherical coordinates?

The derivative in spherical coordinates is important in many fields of science and engineering, including physics, astronomy, and fluid dynamics. It allows for the analysis and optimization of functions in three-dimensional space.

4. Can the derivative in spherical coordinates be expressed in terms of Cartesian coordinates?

Yes, the derivative in spherical coordinates can be converted to Cartesian coordinates using trigonometric identities and the relationship between the two coordinate systems.

5. Are there any limitations to using the derivative in spherical coordinates?

One limitation is that the partial derivatives in spherical coordinates are not always continuous at the origin, which can lead to difficulties in certain calculations. Additionally, some functions may be more complex to differentiate in spherical coordinates compared to Cartesian coordinates.

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