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Evaluating a Derivative Function at a Specified Input

A derivative is itself a function, so $f'$ can be evaluated at any admissible input, and $f'(g(x))$ means the derivative function of $f$ evaluated at the number $g(x)$ rather than the derivative of $f(g(x))$. Covers substituting an expression for the variable inside a derivative and distinguishing 'differentiate then substitute' from 'substitute then differentiate'.

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Find Derivative and Evaluate Function in Calculus using Power Rule at x equals 2

The core principle taught is the application of the power rule for differentiation to compute the derivative of polynomial functions within differential calculus. This procedure relies on formally mu…