Help with Derivative Homework: f(p)/p w.r.t x,y,z

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In summary, the problem is asking for the partial derivatives of f(p)/p with respect to x, y, and z separately, where p = √(x^2 + y^2 + z^2) and f(p) is a scalar function. The solution involves using the chain rule to take the derivatives of f(p) and p with respect to x, y, and z, and then plugging them into the formula for the partial derivative.
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hellsingfan
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Homework Statement



Taking the derivative of f(p)/p with respect to x,y,z separately. p = √(x^2+y^2+z^2) while f(p) is a scalar function that we don't know about

Homework Equations



f(p)/p

The Attempt at a Solution



I just wanted to know if the following is a legitimate way of doing it:

for partial derivative with respect to x: (f'(p)*pxp-f(p)*px)/p2

Similarly for derivative with respect to y: (f'(p)*pyp-f(p)*py)/p2

or is putting f'(p)*px invalid (i was thinking take the derivative of outside multiply by derivative of inside, but I'm not sure if the chain rule can be applied the way I did)
 
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  • #2
hellsingfan said:

Homework Statement



Taking the derivative of f(p)/p with respect to x,y,z separately. p = √(x^2+y^2+z^2) while f(p) is a scalar function that we don't know about

Homework Equations



f(p)/p

The Attempt at a Solution



I just wanted to know if the following is a legitimate way of doing it:

for partial derivative with respect to x: (f'(p)*pxp-f(p)*px)/p2

Similarly for derivative with respect to y: (f'(p)*pyp-f(p)*py)/p2

or is putting f'(p)*px invalid (i was thinking take the derivative of outside multiply by derivative of inside, but I'm not sure if the chain rule can be applied the way I did)

Looks fine so far.
 

1. What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It is calculated by finding the slope of the tangent line to the function at that point.

2. How do I find the derivative of a function f(p)/p with respect to x, y, and z?

To find the derivative of a function with respect to a certain variable, you need to use the chain rule. This means finding the derivative of the numerator with respect to the variable, then dividing it by the original denominator and multiplying it by the derivative of the denominator with respect to the variable.

3. What does it mean to take a derivative with respect to a specific variable?

Taking a derivative with respect to a variable means finding the rate of change of a function in relation to that specific variable. It allows us to understand how the function changes as the variable changes.

4. What is the purpose of finding a derivative?

The purpose of finding a derivative is to help us understand the behavior of a function. It can tell us the slope of the function at a specific point, whether the function is increasing or decreasing, and help us optimize functions in fields such as physics, economics, and engineering.

5. Are there any rules or formulas I need to know to find derivatives?

Yes, there are several rules and formulas that you need to know in order to find derivatives. These include the power rule, product rule, quotient rule, and chain rule. It is important to have a good understanding of these rules and how to apply them correctly.

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