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Flashcards for differentiation and integration.
Differentiation
The process of finding the derivative of a function, which represents the rate of change of the function at a given point.
Derivative of a Function
The derivative measures how the function's output changes concerning its input.
Power Rule
If 𝑓(𝑥) = 𝑥^𝑛, then 𝑓'(𝑥) = 𝑛𝑥 ^𝑛^-^1.
Product Rule
If 𝑓(𝑥) = 𝑔(𝑥) * ℎ(𝑥), then 𝑓'(𝑥) = 𝑔'(𝑥) * ℎ(𝑥) + 𝑔(𝑥) * ℎ'(𝑥).
Quotient Rule
If 𝑓(𝑥) = 𝑔(𝑥) / ℎ(𝑥), then 𝑓'(𝑥) = (𝑔'(𝑥) * ℎ(𝑥) - 𝑔(𝑥) * ℎ'(𝑥)) / [ℎ(𝑥)]^2.
Chain Rule
If 𝑓(𝑥) = 𝑔(ℎ(𝑥)), then 𝑓'(𝑥) = 𝑔'(ℎ(𝑥)) * ℎ'(𝑥).
Implicit Differentiation
A technique used to find the derivative of an implicitly defined function.
Integration
The process of finding the antiderivative of a function.
Indefinite Integrals
Represent a family of antiderivatives or primitives of a function.
Definite Integral
Represents the area between the graph of the function and the x-axis.
Higher Order Derivative
Finding the rates of change of rates of change.
Integration Technique: Substitution
Substituting a new variable to simplify the integrand.
Integration Technique: Integration by Parts
Applying the product rule for differentiation in reverse.
Integration Technique: Partial Fractions
Used for rational functions by decomposing them into simpler fractions.
What terms represent the limits of integration?
a and b
