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Can you explain the concept of derivations?

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Positive and negative square roots

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Q. Can you explain the concept of derivations?

Understand Derivations: Step $1$ : Understand the term ＂derivations＂ in math. Derivations in math usually refer to derivatives, which measure how a function changes as its input changes.
Define Derivative: Step $2$ : Define the derivative of a function. $\newline$ The derivative of a function at a point gives the slope of the tangent line to the function's graph at that point.
Use Limit Definition: Step $3$ : Use the limit definition to find the derivative. $\newline$ For a function $f(x)$ , the derivative $f'(x)$ is defined as: $\newline$ $f'(x) = \lim_{h \to 0} \left[\frac{f(x+h) - f(x)}{h}\right]$
Apply to Simple Function: Step $4$ : Apply the definition to a simple function. $\newline$ Let's find the derivative of $f(x) = x^2$ at $x = 3$ . $\newline$ $f'(3) = \lim_{h \to 0} \frac{(3+h)^2 - 3^2}{h}$ $\newline$ = $\lim_{h \to 0} \frac{(9 + 6h + h^2 - 9)}{h}$ $\newline$ = $\lim_{h \to 0} \frac{(6h + h^2)}{h}$ $\newline$ = $\lim_{h \to 0} [6 + h]$ $\newline$ = $6$

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