Product Rule
Definition
The product rule is a formula used to find the derivative of the product of two functions. It states that the derivative of the product of two functions is equal to the derivative of the first function times the second function, plus the first function times the derivative of the second function.
Analogy
Think of baking cookies. When you mix different ingredients together, you need to follow a recipe and combine them in a specific way. Similarly, when you have two functions multiplied together, you use the product rule to find their derivative by following a specific formula.
Related terms
Chain Rule: The chain rule is used to find derivatives when one function is nested inside another. It allows us to "unwind" layers of functions and find their individual derivatives.
Quotient Rule: The quotient rule is used to find the derivative of a quotient or division between two functions. It helps us determine how changes in one function affect changes in another.
Derivative: A derivative measures how a quantity changes as its input (usually time or position) changes. In calculus, it represents instantaneous rates of change and slopes of curves at specific points.
"Product Rule" appears in:
Study guides (6)
AP Calculus AB/BC - 2.5 Applying the Power Rule
AP Calculus AB/BC - 2.8 The Product Rule
AP Calculus AB/BC - 5.12 Exploring Behaviors of Implicit Relations
AP Calculus AB/BC - 7.2 Verifying Solutions for Differential Equations
AP Calculus AB/BC - 9.1 Defining and Differentiating Parametric Equations
AP Calculus AB/BC - 9.7 Defining Polar Coordinates and Differentiating in Polar Form
Additional resources (1)
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