There are a couple of notations when it comes to denoting the derivative of functions. The most common notations you will see include:

$\bullet$ Leibniz Notation: $\dfrac{d}{dx} f(x)$

$\bullet$ Lagrange Notation: $f'(x)$

$\bullet$ Euler Notation: $D f(x)$

$\bullet$ Newton Notation: $\dot y$

Most likely, you will find Leibniz and Lagrange’s notations being used interchangeably in current day texts. You may find Euler’s notation being used in older textbooks.
Often, you may see a mixture of notations such as in the quotient rule, where it may be easier to use Leibniz’s notation on the left of the equation for clarity, and Lagrange’s notation on the right to save space.
\[\begin{align*}\dfrac{d}{dx} \dfrac{f(x)}{g(x)} = \dfrac{g(x)f'(x) – f(x)g'(x)}{g^2 x}\\\end{align*}\]