Differentiation Rules flashcards

0/14

14 cards remaining

Take the chapter practice test

All 14 cards in this deckShow

What does “Power Rule” mean?Power Product and Quotient Rules: Differentiating a power by multiplying by its exponent and reducing that exponent.
What important condition applies to power rule?Power Product and Quotient Rules: The power rule does not erase the original expression’s domain.
What does “Product Rule” mean?Power Product and Quotient Rules: A sum of two contributions to the rate of a product.
What important condition applies to product rule?Power Product and Quotient Rules: The derivative of a product is not generally the product of derivatives.
What does “Quotient Rule” mean?Power Product and Quotient Rules: A derivative rule for a ratio of differentiable functions.
What important condition applies to quotient rule?Power Product and Quotient Rules: Keep the numerator order and the original nonzero-denominator condition.
What does “Chain Rule” mean?Chain Rule: The derivative of a composition as outer derivative times inner derivative.
What important condition applies to chain rule?Chain Rule: Do not omit the inner derivative.
What does “Multiple Layers of Composition” mean?Chain Rule: Applying the chain rule through nested function layers.
What important condition applies to multiple layers of composition?Chain Rule: Keep the whole inner expression inside the remaining power.
What does “Exponential Derivatives” mean?Derivatives of Exponential and Trigonometric Functions: The local rate of an exponential function, including its input-rate factor.
What important condition applies to exponential derivatives?Derivatives of Exponential and Trigonometric Functions: A general base b adds a factor ln b.
What does “Trigonometric Derivatives” mean?Derivatives of Exponential and Trigonometric Functions: Rates of trigonometric functions under radian input conventions.
What important condition applies to trigonometric derivatives?Derivatives of Exponential and Trigonometric Functions: The standard sine and cosine derivative rules assume radians.