So we all have a basic idea of differentiating rules, for example; both of these hold true
Well it doesn't take much to show both are true. Let's start with
First let's use to the power of both sides to get rid of that
Then use the chain rule and implicit differentiating to get
Rearrange to make the subject
Cancel the and to get
So that's that, but what about ?
First we'll use a natural on both sides
Then differentiate implicitly
Make the subject
That's those two taken care of.
What if we integrate ?
First we need to find a way to integrate . I know let's use integration by parts!
Good, let's make and
So let's work it out then.
That's all for now.