Question

How do you know which rule of differentiation to use?

Answer 1

This answer is a little bit difficult to answer to, as there isn't a unique answer to give. I tried to give a little bit of hints; if you need anything more specific, don't hesitate to ask.

Explanation:

You just need to recognize the case.

One useful thing to keep in mind is that the derivative of a sum is the sum of the derivatives, so if you have more terms you can differentiate them one by one.

The things you'll meet more often are powers of a function and most of all composed function. An example of the first may be `cos^2(x)`, an example of the second `log(3x)`. Of course both things could happen at the same time: `sin^2(4x+2)`.

However, differentiation in general always work like matryoshka dolls: you differentiate the outer content, and then the inner one, applying the basic rules for fundamental functions.