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Calculus Symbols List: How to Read Equations

Calculus > Calculus Symbols List

Calculus is a unique branch of mathematics, and as such it includes many symbols and equations that are also unique. Some are intuitive and make sense at a glance, but others can be very confusing if they are new to you. Here is a quick overview of some of the calculus symbols you will come across.

Common calculus symbols

1. Derivatives

calculus symbols and equations
This is the format for writing a limit in calculus. When read aloud, it says “The limit of the function f of x, as x tends to 0.” (See: What is a limit?)

f'(x)

This is a common symbol indicating the derivative of the function f(x). It reads simply as “The derivative of f of x.” (See: What is a derivative?)

dy/dx

This is another symbol for a derivative. You can read it as “The derivative of y with respect to x.” Y is equivalent to f(x), as y is a function of x itself.

f”(x), d2y/dx

Both of these symbols represent the second derivative of the function, which means you take the derivative of the first derivative of the function. You would read it simply as “The second derivative of f of x.”

fn(x), dn * y/dx

These symbols represent the nth derivative of f(x). Much like the second derivative, you would perform differentiation on the formula for n successive times. It reads as “The nth derivative of f of x.” If n were 4, it would be “The fourth derivative of x,” for example.
y-dot-time-integral
This is the symbol for differentiation with respect to time. You can read it as “the derivative of y with respect to time.”
This is called dot notation; more dots indicate higher orders of differentiation. For example:
2 dots = second derivative.

2. Integrals

integral-symbol-a-to-b
This symbol represents the integration of the function. The integration of the function is essentially the opposite of the differentiation. The variables a and b represent the lower limit and upper limit of the section of the graph the integral is being applied to. If there are no values for a and b, it represents the entire function. You would read it as “The integral of f of x with respect to x (over the domain of a to b.)”

Other Calculus Symbols

Symbol Name Meaning Example
x * y convolution y(t) = x(t)
* h(t)
 
ε epsilon a very small number, close to zero ε 0
e Euler’s number e = 2.718281828… e = lim (1+1/x)x
, x→∞
[a,b] closed interval [a,b] = {x | a x b}  
(a,b) open interval (a,b) = {x | a < x < b}  
i imaginary number i ≡ √-1 z = 4 + 2i
vector    
infinity  

This is just a small sample of the symbols and equations involved in calculus, but should provide a decent launching point for being able to understand calculus symbols and equations.

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Calculus Symbols List: How to Read Equations was last modified: August 14th, 2018 by Stephanie