Subject: Calculus

# Notations

## Notations

Due to the wide application and use of derivatives in mathematics and science learning, there are many symbols and notations, which leaves teachers and students the freedom to choose which one to use. (You can probably guarantee that your teacher will prefer you to use his or her style. Suck up and stick with your teacher's style to gain some brownie points!)

For those of you who just like to know what's out there, a function y=f(x) has the following symbols or notations when asked for its derivatives:

1. f'(x)5. \frac{dy}{dx}
2. D_{x}y6. D_{x}f
3. \frac{d}{dx}[f(x)]7. D_{x}[f(x)]
4. y'

The above notations are just some of the many symbols denoting the derivative of a function. The two famous and most used notations for the derivative is the Newton's notation and Leibniz's notation. There are many controversies, debates and discussions as to whom between Newton and Leibniz were the first to discover differential calculus. That's why we have different versions of the symbols of a derivative. It also adds variety to this seemingly boring subject - thanks to Newton and Leibniz!:-)

### Illustration

In the first section, we have the function f(x)=2x whose derivative is 2. Using the notations outlined above, the derivative of f(x)=y=2x can also be written as;

1. f'(x)=25. \frac{dy}{dx}=2
2. D_{x}y=26. D_{x}f=2
3. \frac{d}{dx}[f(x)]=27. D_{x}[f(x)]=2
4. y'=2

Don't get confused with those notations above. You can pick them up quickly as we go through the subject of differential calculus. Also, you don't need to memorize them all. Even if you remember only one symbol, that's ok. The important thing is to learn how to differentiate a function which will be tackled in the next articles regarding derivative theorems.

### Example #1

When the derivative of f(x) = x with respect to x is 1, which of the following set of notations correctly describes the derivative.

a.) f'(1) = x
b.) f(x)=x
c.) f'(x)=1

c.) f'(x)=1

### Example #2

Which of the following notations are correct when y=x^2?

a.) \frac{dy}{dx} = x^2
b.) f'(x)=y
c.) y'=2x

c.) y'=2x

### Example #3

Which of the following is NOT a notation for derivatives?

a.) \int f(x)
b.) f'(x)
c.) \dot{x}

a.) \int f(x)

### Example #4

Let the function g(x) be defined as 2x, what would be its notation if we get its derivative?

c.) g'(x)=2

### Example #5

Give at least three other form of notations to the derivative in example #4.

\dot{g}=2
D_x [g(x)]=2
\frac{d}{dx}g(x)=2

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