# Lesson 11.11: Caret and Partial Derivative

## The caret

In print the caret is a character that looks like an upside down "v." It may be used for a variety of reasons including to show that a number is being raised to a power. However, in this section we will discuss its use, commonly in statistics, as a "hat." A variable with a caret or "hat" over it may be necessary to distinguish it from other variables. In braille the caret is represented by a dot four five six followed by dot one two six.

In such cases, the caret is positioned directly over the variable. Thus, you must follow the rules in braille for when a character is "directly over" another character. The multipurpose indicator, dot 5, must be placed in front of the variable or character which the caret is over. The multipurpose indicator is then followed by the variable the caret is over. Next will be the directly over indicator (dots one two six) then the braille symbol for the caret. Finally, the caret symbol is followed by the termination symbol.

## The Partial Derivative Symbol

In print, the partial derivative symbol looks like a rounded d. In braille this is represented by a dot four followed by a letter d, or dots one four five.

### Example 1

p with a caret over it or p hat

⠐⠏⠣⠸⠣⠻

### Example 2

q hat

⠐⠟⠣⠸⠣⠻

### Example 3

q hat equals one minus p hat

⠐⠟⠣⠸⠣⠻⠀⠨⠅⠀⠼⠂⠤⠐⠏⠣⠸⠣⠻

### Example 4

open fraction p hat fraction bar q hat close fraction

⠹⠐⠏⠣⠸⠣⠻⠌⠐⠟⠣⠸⠣⠻⠼

### Example 5

the square root of open fraction p hat fraction bar q hat close fraction

⠜⠹⠐⠏⠣⠸⠣⠻⠌⠐⠟⠣⠸⠣⠻⠼⠻

### Example 6

partial derivative of t

⠈⠙⠞

### Example 7

partial derivative of y with respect to x

⠹⠈⠙⠽⠌⠈⠙⠭⠼

### Example 8

the second partial derivative of t

⠈⠙⠘⠆⠐⠞