Mississippi Math C.A.12
The Standard
Use the chain rule and implicit differentiation.
2025 Mississippi College- and Career-Readiness Standards for Mathematics · Use the Definition and Formal Rules of Differentiation to Compute Derivatives
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find derivatives of nested expressions by differentiating the outside, then multiplying by the inside derivative. For equations where y is not isolated, they treat y as a function of x and solve for dy/dx.
What Mastery Looks Like
- A student finds the derivative of (3x²+1)^4 as 24x(3x²+1)^3. For x²+y²=25, they find dy/dx=-x/y and a slope of -3/4 at (3,4).
Common Misconceptions
- Students often forget to multiply by the inside derivative in an expression such as (3x²+1)^4. They may differentiate y² as 2y instead of 2y(dy/dx), or forget to solve for dy/dx.
How to Assess It
- On an exit ticket, ask students to find dy/dx for y=(x²+1)^3 and for x²+y²=25. Have them mark where they used the chain rule in each solution.
Lesson moves
Ways to Teach It
Give pairs cards marked u^4 and u=3x+1; have them arrange the layers and differentiate each before multiplying.
Ask students to explain in writing why differentiating y² in x²+y²=25 gives 2y(dy/dx), while differentiating x² gives 2x.
Post worked derivatives for (2x+1)^3 and x²+y²=25 with missing factors; students race to find and fix the errors.
For a 10-meter ladder, set x²+y²=100; at x=6, find the top's speed if the base slides out at 0.5 meters per second.
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Printable C.A.12 Worksheet
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Related Standards
- C.A.21
Apply the power rule and u-substitution to evaluate indefinite integrals.
- C.A.11
Apply differentiation rules to sums, products, quotients, and powers of functions.
- C.A.20
State and apply the First and Second Fundamental Theorem of Calculus.
- C.A.10
State and apply the formal definition of a derivative.
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