A method used to solve derivatives of composite functions such as: f(x) = sin(x3 + 5)

It can be expressed in two different forms:

f(x) = gI(h(x)) * hI(x)

Or in Leibniz notation as:
dy/dx = (dy/du)(du/dx)

To get the derivative of a composite function you do this:

f(x) = sin(x3 + 5)

We split this into two separate functions:
g(x) = sin(x) and h(x) = x3 + 5

We then find the derivative of each function:
gI(x) = cos(x) and hI(x) = 3x2

Then simply plug them into the formula:
fI(x) = gI(h(x)) * hI(x)
fI(x) = cos(x3 + 5) * 3x2

Note: The chain rule can be applied to composite functions that contain more than just two separate functions like so:

f(x) = (sin(x3))4

We split this into three separate functions:
g(x) = x4 and h(x) = sin(x) and i(x) = x3

We then again find the derivatives of these functions:
gI(x) = 4x3
hI(x) = cos(x)
iI(x) = 3x2

We can then express fI(x) as:
fI(x) = gI(h(i(x))) * hI(i(x)) * iI(x)

Which when we plug the numbers in looks like:
fI(x) = 4(sin(x3))3 * cos(x3) * 3x2


I hate to be nitpicky but izubachi started it.

What you illustrate is not so much that the chain rule can be applied to non-composite functions but rather that all functions can be seen as composites. Which is sort of common sense.

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