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Notation for Differentiation Using First Principles

What is the notation for differentiation using first principles?

In this post, we define the derivative f'(x) from first principles, as lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h} and use the notation for the derivative: \frac{dy}{dx} = f'(x) = y' , where y = f'(x) . This is part of the Prelim Maths Advanced course under the topic Calculus and sub-part The Derivative Function and its Graph, specifically focusing on notation for differentiation using first principles.

 

A guided and clearly explained example of how to set out a differentiation using first principles question.