An alternative notation: f'(x)

Instead of using the notation df/dx to denote the derivative of the function f(x), as we have been doing so far, we can use a simpler notation. The first derivative of the function f(x) is just written as f'(x), where the little line in the air after the f is called a "prime" and the expression is called "f-primed of x".

It is also sometimes called "f-dashed of x".

So if y(x)=sin(x), we can write the derivative as y'(x)=cos(x).

The second derivative has two primes and is called "y double-primed" or "y double dashed": y''(x). And so on.

This notation is obviously more convenient than dy/dx and is very commonly used.