Derivation Rules

Most derivatives of standard functions can be found using a few standard rules. These rules are given in the table below:

Function	Derivative
$a$	$0$
$ax$	$a$
$ax^{2}$	$2ax$
$ax^{n}$	$nax^{n-1}$
$e^{x}$	$e^{x}$
$a^{x}$	$ln(a)a^{x}$
$\sqrt{x} = x^{\frac{1}{2}}$	$\frac{1}{2}x^{-\frac{1}{2}}$
$ln(x)$	$\frac{1}{x}$
$log_{a}(x)$	$\frac{1}{xln(a)}$
$sin(x)$	$cos(x)$
$cos(x)$	$-sin(x)$
$tan(x)$	$\frac{1}{cos^2(x)} = sec^2(x)$
$sin^{-1}(x)$	$\frac{1}{\sqrt{1-x^{2}}}$
$cos^{-1}(x)$	$-\frac{1}{\sqrt{1-x^{2}}}$
$tan^{-1}(x)$	$\frac{1}{1+x^{2}}$

These standard derivatives are useful if a function consists of only one function, or a sum of several functions and they can be used to solve almost every derivative. However, when a function is multiplied or divided by another function, this new function requires extra techniques for finding the derivative of that function. These techniques are explained in the next articles: Product Rule, Qoutient Rule and Chain Rule.

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