# Understanding Partial Derivatives: A Visual Explanation

• O.J.
In summary, the conversation discusses the concept of partial derivatives in the context of a physics course. It is explained that partial derivatives are similar to regular derivatives, but with the other variables held constant. An example is given with the derivative of Cx^4, where C is replaced with a different variable. The conversation ends with the suggestion to visualize the concept with a solid shape being chopped into two pieces.
O.J.
OK, they're throwing pretty weird concepts to our heads in this PHY101 course. stuff like even partial derivatives that we didnt take in math. differentiating partially with respect to a single variable treating others as contants is NOT getting through my head. can someon PLEASE illustrate it for me?

partial derive of xyz with respect to y (say) is as if z and x are just numbers
so you get xz*1= xz.

Say you replaced every other variable with a fixed number except the var. you differentiate. It is then just regular derivatives. Remember calc 1? What is the deriv. (w/ resp. to x) of Cx^4 ...ANS> C*4*x^3. Now, change C to another variable y,z,w ...whatever.. same math.

Hope it helps.

$$E_p(k_X, k_Y) = \iint E_s(x,y)e^{i(xk_X+yk_Y)}\,dx\,dy$$

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heh, wish I knew what text you were using, I was looking for a phy101 that does exactly this(but that it does it without warning you before you enroll is pretty nasty)

gammamcc said:
partial derive of xyz with respect to y (say) is as if z and x are just numbers
so you get xz*1= xz.

Say you replaced every other variable with a fixed number except the var. you differentiate. It is then just regular derivatives.

Remember calc 1? What is the deriv. (w/ resp. to x) of Cx^4 ...ANS> C*4*x^3. Now, change C to another variable y,z,w ...whatever.. same math.

Hope it helps.

pretty sure he doesn't get the concept but he knows how to do it.

It's like the derivative wrt x (say) along a curve where z,y are constant. Drawing a picture will make it easy straight away. Think of a solid shape. Chop it into two pieces. The rate of change along the edge is kind of doing a partial derivative.

## 1. What are energy functions in science?

Energy functions are mathematical equations that describe the relationship between energy and other variables, such as position, velocity, and time. They are used to model and predict the behavior of physical systems, such as atoms and molecules.

## 2. How do energy functions help scientists?

Energy functions help scientists understand and predict the behavior of physical systems by providing a mathematical framework for describing energy and its effects. They allow scientists to make predictions and test hypotheses about the behavior of energy in different systems.

## 3. What types of energy functions are there?

There are many different types of energy functions, such as potential energy functions, kinetic energy functions, and thermodynamic energy functions. These functions can be used to describe different types of energy, such as mechanical, electrical, and thermal energy.

## 4. Can energy functions be used to solve real-world problems?

Yes, energy functions are used in many real-world applications, such as designing new materials, developing new technologies, and understanding the behavior of complex systems. They are also used in fields such as physics, chemistry, and engineering to solve practical problems.

## 5. Are there any limitations to using energy functions?

While energy functions are a useful tool for understanding and predicting the behavior of physical systems, they do have some limitations. For example, they may not accurately describe the behavior of complex systems, and they may not take into account all factors that can affect energy in a given system.

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