Definition
Let us consider a function $\rm{f(x)}$ continuous in a interval $\rm{(a,b)}$ then the derivative of the function $\rm{f}$ at a point $\rm{x, x \in (a,b)}$ is defined as
$$\rm{\lim_{\triangle x \to 0} \frac{f(x + \triangle x) - f(x)}{\triangle x}}$$
provided the limit exists.
If a is a fixed point then, the derivative of f(x) at x = a denoted by f'(a) is defined by
$$\rm{\lim_{x \to a} \frac{f(x) - f(a)}{x - a}}$$
Representation of derivative of a function f with respect to x
Any of the following symbols can be used to find the derivative of a function y = f(x) with respect to x
$$\rm{f'(x)}, \rm{\frac{d}{dx} f(x)}, \rm{y'}, \rm{\frac{d}{dx}(y)}$$