Differentiation by first principles, also known as the definition of the derivative, involves finding the derivative of a function f of x using the limit process. It is defined as:

f prime of x equals the limit as h approaches zero of the difference f of x plus h minus f of x divided by h

This approach calculates the instantaneous rate of change of the function at a specific point. The numerator represents the change in the function's value, and the denominator represents the change in the input h approaching zero. By applying this limit, we obtain the derivative, which provides the slope of the tangent line to the function at any point x.

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