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

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SUMMARY

The discussion clarifies the distinction between the curly (∂) and derivative (d) signs in calculus, specifically in the context of multivariable functions. The curly sign represents a partial derivative, indicating the derivative of a function with respect to one variable while holding others constant. The expression dE refers to the total differential, which can be derived by summing the partial derivatives of E with respect to each variable k. This concept is fundamental in multivariable calculus and is essential for understanding energy functions in physics.

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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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