Note: In this section, assume all functions are differentiable with respect to $x$.
The process of finding the derivative function using the definition
\[\mathrm{f }'\left( x \right)=\underset{\Delta x\,\to \,0}{\mathop{\lim }}\,\frac{\mathrm{f }\left( x+\Delta \,x \right)-\mathrm{f }\left( x \right)}{\Delta \,x}\]
is called differentiating from first principles.

Note: In this section, assume all functions are differentiable with respect to $x$.

The process of finding the derivative function using the definition

\[\mathrm{f }'\left( x \right)=\underset{\Delta x\,\to \,0}{\mathop{\lim }}\,\frac{\mathrm{f }\left( x+\Delta \,x \right)-\mathrm{f }\left( x \right)}{\Delta \,x}\]

is called differentiating from **first principles.**

Techniques of Differentiation - Differentiation by First Principles

Techniques of Differentiation - Differentiation by First Principles