Class Notes – Differentiation (Year 12 Further Maths)

Differentiation of Standard Functions

If $y = x^n$ then,

$\frac{dy}{dx} = nx^{n-1}$ ,

where $n$ is a constant.
If $y = kx^n$ then,

$\frac{dy}{dx} = knx^{n-1}$ ,

where $k$ and $n$ are constants.
If $y = k$ then,

$\frac{dy}{dx} = 0$ ,

where $k$ is a constant.
If $y = ax^m + bx^n + cx^p$ + …….. then,

$\frac{dy}{dx} = amx^{m-1}$ + $bnx^{n-1}$ + $cpx^{p-1}$ + ……,

where $a$ , $b$ , $c$ , $m$ , $n$ , $p$ , …. are constants.

You can differentiate this way only if terms are added or subtracted.