Florida B.E.S.T. MA.912.C.2.4
The Standard
Apply the rules for finding derivatives of constants, sums, products, quotients and the Chain Rule to solve problems with functions limited to algebraic, trigonometric, inverse trigonometric, logarithmic and exponential.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify which differentiation rules a function requires and apply them in the correct order. They differentiate algebraic, trigonometric, inverse trigonometric, logarithmic, and exponential functions, including combinations and compositions.
What Mastery Looks Like
- Students correctly differentiate functions that combine several operations and function types. They choose each rule in the right order, include inner derivatives, and simplify the result accurately.
Common Misconceptions
- Students often multiply derivatives instead of using the product rule. They may forget to square the denominator in the quotient rule or omit the inner derivative in a composite function. Logarithmic, exponential, and inverse trigonometric formulas are also commonly mixed up.
How to Assess It
- Use this exit ticket: Differentiate f(x) = [(x² + 1)sin(3x)]/eˣ, then label every rule used. Differentiate g(x) = arctan(2x).
Lesson moves
Ways to Teach It
Give pairs function cards and derivative-rule cards, then have them match each function to the rules needed before differentiating.
Ask students to explain why the derivative of f(x)g(x) is not simply f′(x)g′(x), using a numerical example.
Run a derivative relay where teams solve one step of a multirule derivative, check it, then pass it to the next student.
Model changing temperature with T(t) = 70 + 20e⁻⁰·²ᵗ, then find and interpret T′(5) with units.
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Related Standards
- MA.912.C.1.2
Determine the value of a limit if it exists algebraically using limits of sums, differences, products, quotients and compositions of continuous functions.
- MA.912.C.3
Apply derivatives to solve problems.
- MA.912.C.2.3
Prove the rules for finding derivatives of constants, sums, products, quotients and the Chain Rule.
- MA.912.C.4.2
Apply Riemann sums, the Trapezoidal Rule and technology to approximate definite integrals of functions represented algebraically, geometrically and by tables of...
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