Finding dE/dx: Using the Chain Rule

In summary, the conversation discusses the use of the chain rule in finding dE/dx and dt'/dx in question 16b of a given link. The chain rule is used to find derivatives of functions with multiple variables, but in this case, t' is not a function of x, causing confusion on why its derivative is being taken with respect to x.
  • #1
mrmojorizing
7
0
Hi fi you look at quesiotn 16b in the following link they try to find dE/dx.

they use the chain rule. the chain rule says dF/dt=dx/dt*dF/dx+dy/dt*dF/dy if F=f(x,y) and x=f(t) and y=f(t).

But in 16b they're trying to find dE/dx and as part of the use of the chain rule they try to find dt'/dx (in the first equation under where it says 'a galilean transform...') however t' is not a function of x, so i don't understand why they're taking the derivative of t' wrt to x.


http://stuff.mit.edu/afs/athena/course/8/8.20/www/sols/sol1.pdf
 
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  • #2
That's very simple,
[tex]\frac{\partial t'}{\partial x}=0.[/tex]
 

1. What is the chain rule?

The chain rule is a calculus rule that is used to find the derivative of a composite function. It states that the derivative of a composite function is equal to the derivative of the outer function multiplied by the derivative of the inner function.

2. Why is the chain rule important?

The chain rule is important because it allows us to find the derivative of more complex functions by breaking them down into simpler functions. It is a fundamental rule in calculus and is used in many real-world applications.

3. How do you use the chain rule to find dE/dx?

To find dE/dx using the chain rule, you first need to identify the composite function and its inner and outer functions. Then, you can apply the chain rule by taking the derivative of the outer function and multiplying it by the derivative of the inner function. Finally, you can substitute the variable x back into the resulting expression to get dE/dx.

4. What are some common mistakes when using the chain rule?

One common mistake when using the chain rule is forgetting to take the derivative of the outer function. Another mistake is not correctly identifying the inner and outer functions, which can lead to incorrect results. It is also important to pay attention to the order of operations when applying the chain rule.

5. How can I practice using the chain rule to find dE/dx?

You can practice using the chain rule to find dE/dx by solving various problems and working through examples. There are also many online resources and practice exercises available that can help you improve your understanding and application of the chain rule.

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