Instructional priorities

• Begin with multiple representations and precise language.
• Require theorem or definition names when they govern a conclusion.
• Use technology after a mathematical setup is visible.
• Assess notation, units, interpretation, and verification—not answers alone.

Evidence cycle

1. Readiness retrieval
2. Guided concept development
3. Pathway practice
4. Investigation
5. Mastery attempt
6. Correction and reassessment

Common misconceptions

Differentiating only the outer function omits the inner rate and produces the wrong scale. A y-term is not constant during implicit differentiation. The inverse derivative is not simply 1/f'(a); the original derivative must be evaluated at f^{-1}(a). After finding y'/y, the final derivative still requires multiplication by y.

Assessment guidance

Use the teacher keys as instructional references. Accept mathematically equivalent exact forms. Require work for formal evidence and inspect calculator or CAD settings when technology affects the result.