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), d^{2}y/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.”

## f^{n}(x), d^{n} * 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**.