First Principle (definition) of Differentiation

Please look carefully the following operations in order to get a comprehensive understanding of principle of differentiation:

WE ARE FINDING THE INSTANTANEOUS SLOPE AT A PARTICULAR POINT ON THE GRAPH.

Can’t get it? Let’s look at some typical examples.

You need to have basic ideas of binomial theorem for this example. If you are not sure, click Binomial Theorem.

For one more example: this time y=ln x

You also need some background knowledge about the number e. Click here.

This is why e is so intriguing to mathematicians with the logarithm of its base having this fascinating derivative.

Sometimes for other functions, it may not be easy to differentiate with direct methods.

Some common rules (proof omitted):

These are, respectively, called sum, product, chain and reciprocal rules.

The next page is a list of formulae convenient for any finding of the derivatives without proof.