AP Calculus BC · Unit 2
Differentiation: Definition and Fundamental Properties
In short
Unit 2: Differentiation: Definition and Fundamental Properties in AP Calculus BC covers 10 topics: Defining Average and Instantaneous Rates of Change at a Point, Defining the Derivative of a Function and Using Derivative Notation, Estimating Derivatives of a Function at a Point, Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist and 6 more. Open each one for what you need to know, a self-check list and how it is tested on the exam.
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What is in Unit 2: Differentiation: Definition and Fundamental Properties?
Unit 2: Differentiation: Definition and Fundamental Properties
2.1 Defining Average and Instantaneous Rates of Change at a Point
- I can express the instantaneous rate of change of a function at x = a using the limit definitions of the derivative.
2.2 Defining the Derivative of a Function and Using Derivative Notation
- I can recognize and use various notations for the derivative, including dy/dx, f'(x), and y'.
- I can represent the derivative graphically, numerically, analytically, and verbally.
- I can relate the derivative of a function at a point to the slope of the tangent line at that point.
2.3 Estimating Derivatives of a Function at a Point
2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
- I can state that if a function is differentiable at a point, it must be continuous at that point, and that a point outside the domain of a function is also outside the domain of its derivative.
- I can recognize and provide examples of continuous functions that fail to be differentiable at a point in their domain (e.g., corners, cusps, vertical tangents).
2.5 Applying the Power Rule
- I can use the power rule to calculate the derivative for functions of the form f(x) = x^r.
2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
2.7 Derivatives of cos x, sin x, e^x, and ln x
- I can calculate the derivatives of sine, cosine, exponential, and logarithmic functions.
2.8 The Product Rule
- I can apply the product rule to find the derivative of a product of functions.
2.9 The Quotient Rule
- I can calculate the derivative of a quotient of differentiable functions using the quotient rule.
2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
Differentiation: Definition and Fundamental Properties: common questions
What is in Unit 2: Differentiation: Definition and Fundamental Properties?
It covers 10 topics: 2.1 Defining Average and Instantaneous Rates of Change at a Point; 2.2 Defining the Derivative of a Function and Using Derivative Notation; 2.3 Estimating Derivatives of a Function at a Point; 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist; 2.5 Applying the Power Rule; 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple; 2.7 Derivatives of cos x, sin x, e^x, and ln x; 2.8 The Product Rule; 2.9 The Quotient Rule; 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions.
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