What does Differentiate actually mean?

[Hantoo]

What does Differentiate actually mean?
in my math class... i know if i differentiate an equation, i can get the gradient function for tangent to the curve at whenever point...

but how does this method works.. I mean.... when Differentiate, why you have to do this and do that... and what it does?

 

[Vinz]

"How do you find a rate of change, in any context, and express it mathematically? You use differentiation. "
http://www.mathtutor.ac.uk/differentiation

 

[Hantoo]

thanks!