NZ Level 7 (NZC) Level 2 (NCEA)
Notations for the derivative (investigation) LIVE
Lesson

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:

• Differentiate
• Find the derivative of ...
• Find the gradient function for ....

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

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

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

### Outcomes

#### M7-10

Apply differentiation and anti-differentiation techniques to polynomials

#### 91262

Apply calculus methods in solving problems