Algebra 2 & Pre-Calculus – Honors
Section 34
The Chain Rule
Derivative Investigations
Common Core Standards

This section is taught in preparation for a calculus class, which goes beyond the scope of the common core
standards.
Mathematical Practice Standards
MP1: Make sense of problems and persevere in solving them.
MP7: Look for and make use of structure.
MP3: Construct viable
arguments and critique the
reasoning of others.
MP4: Model
with
mathematics.
MP5: Use
appropriate tools
strategically.
MP6: Attend to
precision.
Previous Experience



Students have extensive experience with composition of functions from A1H and A2PCH.
Students studied polynomial functions in factored (or easily factored) form in A1H.
Students have experience with polynomial, product, and quotient rule from A2PCH.
Objective(s)


Find the derivative of the composition of two functions… f g  x 

New Vocabulary

chain rule
Rationale

The chain rule is both a fundamental method of differentiation, as well as an opportunity to solidify other methods
of differentiation (polynomial, product, quotient rules).
Teacher Notes

Recommended Video: http://www.calculus-help.com/the-chain-rule/
o This should be shown after reviewing composition of functions.
o The functions shown in the video (sin x and ln x) serve as previews of upcoming differentiation. It would
be good to let students know before the video:

f  x   sin x  f '  x   cos x
1
x
End the video after the ‘official scary’ definition (omit the exercise)



o
Day 1
o
Day 2
o
f  x   ln x  f '  x  
Simplification – While simplification is not necessary, the following is recommended (to make evaluation
easier)
 No negative exponents in answers
 Return fractional exponents to radical form
Similar to A1H, polynomials in AP Calculus are often presented in factored (or easily factored form).
Derivatives of polynomials in this format are common.