Trick to Solving Differential Calculus

 Have you ever wondered why our professors teach the very basic idea of differentiating an equation by memorizing the formula below? 

And, if you are given a task to differentiate d/dx (x^3), the first way we will approach it is like this (by using the formula above):

And, if we are going to dig deeper and check the proof of this formula, we can deduce that:

With this in mind, we can now use this shortcut way of differentiating a simple equation below:

Voila! Here you go, you can now use the short method for differentiating basic equations such as shown above. :)