2. The chain rule basically deals with functions
within a function. There is a strong
relationship between them. If you consider
the links on a chain, one link overlaps the
other.
If there is a change to either the inside or
outside link, it affect the relationship between
them.
3. I believe so far that you have covered
derivatives of functions. For example y =f(x)
and dy/dx = f’(x).
But now considertwo functions f(x) and g(x).
We will loo at a function within a function.
For instance y = f(g(x)). So then what is y’?
The chain rule is what is applied!!
4. If y = f(g(x))
y’= f ’(g(x)) . g’(x) OR
Alternatively
You can let u = g(x) and so it becomes
y = f(u)
And then to determine y’, we get
y’ = dy/dx = dy/du * du/dx.
5. It can also be written as
y’ = dy/dx = du/dx * dy/du
6. A simple example could be
y = (2x +5)2
Let u = 2x +5 therefore y =u2
du/dx = 2 + 0 =2
dy/du = 2u1 = 2(2x +5)
Therefore dy/dx = dy/du *du/dx
= 2*2(2x +5)=4(2x + 5)
= 8x + 20