Mississippi Math C.A.11
The Standard
Apply differentiation rules to sums, products, quotients, and powers of functions.
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 expressions that add, multiply, or divide functions. They also differentiate powers of functions, including the derivative of the expression inside the power.
What Mastery Looks Like
- A student can differentiate (x²+1)(x+3), (x²+1)/(x+3), and (x²+1)³ without dropping terms. They can name the rule used at each step.
Common Misconceptions
- Students often turn the derivative of a product into the product of the derivatives. They may divide derivatives to handle a quotient or leave out the inner derivative when differentiating (x²+1)³.
How to Assess It
- Exit ticket: Differentiate y=(x²+1)²(x+3)/(x−1). Label where you use the product, quotient, and chain rules.
Lesson moves
Ways to Teach It
Give pairs cards labeled f=x²+1 and g=x+2; have them arrange rule cards to find derivatives of f+g, fg, and f/g.
Ask students to explain in writing why the derivative of (x²+1)³ needs a factor of 2x.
Time pairs as they sort x²+3x, x²(x+1), x²/(x+1), and (x²+1)³ by rule, then find each derivative.
Use a ticket revenue model R(p)=p(100−2p); have students find R'(p) and the ticket price that gives the most revenue.
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