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

[masyousaf1]

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

 

[RaulTheUCSCSlug]

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.

 

[RaulTheUCSCSlug]

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!

 

[Khashishi]

This subject is covered in multivariable calculus

 

[masyousaf1]

Thanks RaulTheSCSlug, kindly mention what is the physical meaning of the quantity ∂E/∂k₁ * dk₁ .

Best wishes