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AP Calculus AB›Unit 2: Differentiation: Definition and Fundamental Properties›The derivative

Differentiability and Continuity

Differentiable implies continuous, but not the other way around: corners, cusps, and vertical tangents are continuous but have no derivative.

Where derivatives fail
Corners, cusps, vertical tangents
Piecewise differentiability

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2Differentiation: Definition and Fundamental Properties

Average and Instantaneous Rates of Change
The Definition of the Derivative
Estimating Derivatives from Graphs and Tables
Differentiability and Continuity
The Power Rule
Derivatives of sin x, cos x, eˣ, and ln x
Product and Quotient Rules
Derivatives of tan, cot, sec, and csc

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The Power Rule

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Also called: differentiability, differentiable vs continuous, corner cusp