Students demonstrate an understanding of the formal definition of the derivative of a function at a point and the notion of differentiability:
Lessons for this standard
More specific sub-standards
Students demonstrate an understanding of the derivative of a function as the slope of the tangent line to the graph of the function.
Students demonstrate an understanding of the interpretation of the derivative as an instantaneous rate of change. Students can use derivatives to solve a variety of problems from physics, chemistry, economics, and so forth that involve the rate of change of a function.
Students understand the relation between differentiability and continuity.
Students derive derivative formulas and use them to find the derivatives of algebraic, trigonometric, inverse trigonometric, exponential, and logarithmic functions.