Derivatives quiz
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How does a curve slope if its derivative is positive?
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More questions about Derivatives
These visible examples show the question style. LearnClash turns the full topic into ranked duels and spaced repetition.
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What operation reverses differentiation?
Answer: Integration
Why: The fundamental theorem of calculus links derivatives and integrals by showing they directly undo each other.
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What is the derivative of a line $y = mx + b$?
Answer: $m$
Why: Straight lines never curve, so the derivative simplifies directly to the slope $m$ without needing any variables.
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How is the derivative of a fraction calculated?
Answer: Quotient rule
Why: The quotient rule squares the denominator while computing $f'g - fg'$ across the numerator.
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What mark indicates a derivative in $f'(x)$?
Answer: Prime
Why: Joseph-Louis Lagrange introduced the prime tick mark in 1770 to simplify writing derivatives without fractions.
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What is the derivative of $e^x$?
Answer: $e^x$
Why: For $e^x$, the slope of the curve at any point exactly equals the value of the function at that same point.
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What quantity is the derivative of position over time?
Answer: Velocity
Why: Differentiating position with respect to time gives velocity, and differentiating again gives acceleration.
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