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.
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- What is a derivative?
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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?
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The slope of the tangent line to the function's graph at a given point- What is the notation f'(x) used for?
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The derivative of the function f with respect to x- What is the Power Rule for derivatives?
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The derivative of x^n is n times x^(n-1)- What is the derivative of a constant?
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Zero- What is the Constant Multiple Rule for derivatives?
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The derivative of c times f(x) is c times f'(x)- What is the Sum Rule for derivatives?
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The derivative of a sum of functions is the sum of their derivatives- What is the Difference Rule for derivatives?
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The derivative of a difference of functions is the difference of their derivatives- What is the derivative of sin(x)?
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cos(x)- What is the derivative of cos(x)?
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negative sin(x)- What is the derivative of e^x?
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e^x- What is the derivative of ln(x)?
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1 divided by x- What does it mean for a function to be differentiable at a point?
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Its derivative exists at that point- What is a necessary condition for a function to be differentiable at a point?
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The function must be continuous at that point- Can a continuous function fail to be differentiable at a point?
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Yes, such as at a sharp corner or a vertical tangent
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