What are the steps behind differentiating and simplifying the following:

y = sin^3x

In getting y' = 3sin^2xcosx why do we not get cos^2x?

By using the chain rule.



The derivative of the inside times the derivative of the outside.

The derivative of the outside is

The derivative of the inside is

We get the cos(x) by just differentiating sin(x).

You can also have it with the product rule.

You know that ?

Then put it like that:

Use the product rule here;