Working with symbolic expressions

Using the formula editor: Working with symbols

Working with symbolic expressions

Mathematical formulas consist of more than just numbers: usually there are symbols present. Think of variables, names of physical quantities, names of functions, etcetera. To enter a mathematical formula you can use a keyboard and/or the formula editor. The table below lists the most common mathematical symbols and the syntax for entering them.

Symbol	Syntax	$\phantom{x}$ Description
$\cos(x)$	`cos(x)`	$\phantom{x}$ cosine of $x$
$\sin(x)$	`sin(x)`	$\phantom{x}$ sine of $x$
$\tan(x)$	`tan(x)`	$\phantom{x}$ tangent of $x$
$\ln(x)$	`ln(x)`	$\phantom{x}$ natural logarithm of $x$
$\log_{a}(x)$	`log(a,x)` or `log_a(x)`	$\phantom{x}$ logarithm of $x$ with base $a$
$x^y$	`x^y`	$\phantom{x}$ $x$ to the power $y$
$e^x$	`e^x` or `exp(x)`	$\phantom{x}$ $e$ -power of $x$ , exponential function
$\sqrt{x}$	`sqrt(x)` or `x^(1/2)`	$\phantom{x}$ square root of $x$
$\sqrt[n]{x}$	`x^(1/n)`	$\phantom{x}$ $n$ -th root of $x$
$\|x\|$	`abs(x)`	$\phantom{x}$ absolute value of $x$
$\displaystyle \frac{x}{y}$	`x/y`	$\phantom{x}$ $x$ divided by $y$
$x\cdot y$	`x*y`	$\phantom{x}$ product of $x$ and $y$
$\pi$	`pi`	$\phantom{x}$ the constant $\pi$

There are a few things you should pay special attention to. The main rule is:

Rule

Almost always use the multiplication sign *

The only exception to the above rule is when an integer is followed by a letter or known symbol such as in $2x$ and $2\pi$ .

xy is a name consisting of two characters; x*y is the product of two variables.
x2 is a name consisting of a letter followed by a number; x*2 is the product of a variabele and a number.
By the way, the system often warns its user when names consisting of two letter are entered:

Also in case of brackets it is often necessary to enter a multiplication symbol:
So not 2(x+1) and(x+1)x, but (x+1)*x to denote a factorized expression.

f(x-1) usually indicates a function call with argument x-1, but it can also be read as a product of f and x-1; in case of f*(x-1), there is no doubt anymore, because this is certainly a product.