So far we have seen only one type of notation for the derivative. But there are a number of different notations (all with their special part in history).
These phrases all require the same process to be carried out:
These notations are all used for the result of differentiating:
$y'$y′ | pronounced $y$y dash, or $y$y prime | |
$f'$f′ | pronounced $f$f prime | |
$f'(x)$f′(x) | pronounced $f$f dash of $x$x, or $f$f prime | |
$\frac{dy}{dx}$dydx | pronounced dee $y$y dee $x$x. | |
$\frac{d(f(x))}{dx}$d(f(x))dx | pronounce dee by dee $x$x of $f$f of $x$x |
Leibniz's notation is this one: $\frac{dy}{dx}$dydx and $\frac{d(f(x))}{dx}$d(f(x))dx. Leibniz was a German mathematician and philosopher, and predominantly due to his work in the field of calculus, holds a prominant place in the history of mathematics. Leibniz's notation is the original notation.
We can also use Leibniz's notation to demonstrate the evaluation of the derivative at point, like this
This means evaluate the derivative dee $y$y by dee $x$x at the point where $x$x is equal to $a$a.
Lagrange's notation is one of the most commonly used in calculus. Lagrange was an Italian mathematician and astronomer who made popular this notation.
$f'$f′ and $f'(x)$f′(x)
We can also use Lagrange's notation to demonstrate the evaluation of the derivative at point, like this
$f'(a)$f′(a), which means evaluate the derivative $f$f dash of $x$x, at the point where $x$x is equal to $a$a.
Apply differentiation and anti-differentiation techniques to polynomials
Apply calculus methods in solving problems