What is the difference between curly and derivative (d) sign

AI Thread Summary
The discussion clarifies the difference between the curly sign (∂) and the derivative sign (d), with the curly sign representing a partial derivative used for functions of multiple variables. The expression dE relates to taking the partial derivative of energy (E) with respect to each variable (k) and summing them, as per multivariable calculus principles. Additionally, the physical meaning of the quantity ∂E/∂k1 * dk1 is requested for further clarification. Understanding these concepts is essential for analyzing functions in physics and mathematics. The conversation emphasizes the importance of partial derivatives in multivariable contexts.
masyousaf1
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Dear All,

Please see the image below in attachment where Energy is function of K. I want to understand how is it possible to understand the last expression ( dE = ? ). Additionally, what is the difference between curly and derivative (d) sign ?

Many thanks to the mentors on this forum
Best wishes
 

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the "curly" derivative (d) sign is called a partial derivative, and is when you only take derivative of a function that has multiple variables. It works very similar to a regular derivative.
 
The last expression is just taking the partial derivative of E with respect to each k, and summing them up since the derivative of the sum is the sum of derivatives!
 
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This subject is covered in multivariable calculus
 
Thanks RaulTheSCSlug, kindly mention what is the physical meaning of the quantity ∂E/∂k1 * dk1 .

Best wishes
 

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