Derivatives
What is Derivatives?
The derivative is the instantaneous rate of change of a function with respect to one of its variables. This is equivalent to finding the slope of the tangent line to the function at a point. Let's use the view of derivatives as tangents to motivate a geometric definition of the derivative.
The derivative of \(f\left( x \right)\) with respect to x is the function \(f'\left( x \right)\) as, $$\begin{equation}\mathop {\lim }\limits_{h \to 0} \frac{{f\left( {a + h} \right) - f\left( a \right)}}{h} \end{equation}$$
Example of Derivatives
$$\frac{d}{dx} (\log_5 (x))^{x/2}$$