Chain Rule
One of the core principles in Calculus is the Chain Rule.
Refer to Khan academy article: Chain rule ▶ Proceed to Integral rule of composite functions: U-substitution
It tells us how to differentiate Composite functions
.
Common mistakes
Not recognizing whether a function is composite or not
Wrong identification of the inner and outer function
Forgetting to multiply by the derivative of the inner function
Computing
f(g(x))
wrongly:
How to identify Composite functions
Seems a basic algebra101, but actually a quite tricky one to identify.
Refer to Khan lecture: Identifying composite functions
The core principle to identify it, is trying to re-write the function into a nested one: f(g(x))
. If you could do this, it's composite, if not, then it's not one.
Examples
Two forms of Chain Rule
Two forms of Chain Rule
Their results are exactly the same. It's just some people find the first form makes sense, some more people find the second one does.
Example
Chain rule for exponential function
Chain rule for exponential function
Example
Apply the
Log power rule
to simplify the exponential function:Differentiate both sides:
Last updated