# How to Read Symbols and Equations in Calculus

Calculus > How to Read Symbols and Equations

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 when you are not instructed on what they mean. Here is a quick overview of some of the symbols you will come across in calculus.

## Common Symbols and Equations in Calculus

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.”

## 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.”

## 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.

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.)”

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 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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