00:01
So, things are getting a
little bit more exciting now.
00:05
We're going to start to look
at three new rules.
00:08
We'll look at
the chain rule, the product rule,
and the quotient rule.
00:12
And we'll talk about
when to use them,
and what kind of functions
we need to look at
in order to use those rules.
00:18
Now, remember, previously,
you've learned how to differentiate
from first principles,
we've learned how to differentiate
the faster way,
and we've also looked
at the applications
of differentiation.
00:27
So we've looked at finding
the gradient of a tangent,
the gradient of a normal,
and also move to finding equations
of tangents and normals.
00:36
So let's start looking
at our three new rules.
00:39
The principles here
are the three different
types of functions
that we'll be looking at.
00:45
The first type of function is called
a function of a function.
00:48
I'll explain what that means better
as we go through numerical examples.
00:52
But what that really is, is a
function inside of another function.
00:56
And you can have a chain of
different functions.
00:58
And we also refer to this
as the chain rule as well.
01:02
The second type of function
that we'll be looking at
is just a product of two functions.
01:06
So that's fairly
straightforward to spot.
01:08
You just look at two functions
that are multiplying together.
01:11
And then we'll talk about
what rule to use
to differentiate it.
01:15
And the last type,
which is predictable
is going to be two functions
which are dividing each other.
01:19
so you have one on top
of the other.
01:21
And then we'll look at the rules
that we need
to differentiate a function,
which is a quotient.
01:26
We call it one above the other
or dividing it.
01:30
The techniques for each one
for a function of a function
is the chain rule,
because it's a function
within a function.
01:37
When you have
the product of two functions,
we just call it the product rule.
01:40
And when you have
two functions dividing,
we call it the quotient rule.
01:45
So we'll learn how to apply them.
01:46
And we'll also look at
the derivatives
and the proofs for them.
01:50
So you're fully convinced
that it's the right thing to do.
01:53
And the applications once again,
we're differentiating.
01:55
So we're going to be finding
the gradient of course,
with the gradient,
we can do lots of other things,
we can find the equations
of tangents and lines,
and we'll move on defining
stationary points of curves as well.
02:07
So let's start and look at
our first problem.