How to Differentiate Equations

Differentiation may seem very confusing at first but it is actually very simple and easy as long as you follow these short instructions.

Differentiation is used to find the gradient in most cases of a graph at a specific point. This is done by finding the dy/dx and the substituting into the new equation an x value to find the gradient at that point.

Here are the short tips to make differentiation easy:


1) Make the equation as simple as you can make it. 


This is done by making the coefficients of x nice numbers and the same with the powers of x. This requires indices rules. For example:




As you can see when given an equation you want to make it as simple as possible. This will make things A LOT easier.

Here is an example of an equation of a line that becomes much more simplified:






2) Multiply the coefficient of x by the power (coefficient means the number before the x!)

This is quite a straightforward step:

In this step you do not want to change the value of  anything except the coefficient of x.

3) Minus 1 from the power!

This can be done as shown:






And that's it! This is an example of an actual question with all the steps:

1)  Original equation



2)  Simplifying values of x


3)  Multiplying the power by the coefficient

Note - anything to the power of 0 = 1

4)  Minus 1 from the powers of x

5)  Easy peasy :)