AP Calculus AB, unit: Differentiation: Definition and Fundamental Properties. Conceptual understanding and key rules for this unit, explained in plain language alongside the formula. Front: a concept or short problem cue. Back: the explanation, rule, or answer.
19 cards · basic cards · AI-written, checked twice. Edit anything.
- What is a derivative?
- A measure of how a function's output changes with respect to a small change in its input
- What does the derivative of a function represent geometrically?
- The slope of the tangent line to the function's graph at a given point
- What is the notation f'(x) used for?
- The derivative of the function f with respect to x
- What is the Power Rule for derivatives?
- The derivative of x^n is n times x^(n-1)
- What is the derivative of a constant?
- Zero
- What is the Constant Multiple Rule for derivatives?
- The derivative of c times f(x) is c times f'(x)
- What is the Sum Rule for derivatives?
- The derivative of a sum of functions is the sum of their derivatives
- What is the Difference Rule for derivatives?
- The derivative of a difference of functions is the difference of their derivatives
- What is the derivative of sin(x)?
- cos(x)
- What is the derivative of cos(x)?
- negative sin(x)
- What is the derivative of e^x?
- e^x
- What is the derivative of ln(x)?
- 1 divided by x
- What does it mean for a function to be differentiable at a point?
- Its derivative exists at that point
- What is a necessary condition for a function to be differentiable at a point?
- The function must be continuous at that point
- Can a continuous function fail to be differentiable at a point?
- Yes, such as at a sharp corner or a vertical tangent
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