Derivatives are the rates at which quantities change. They measure how a function behaves as its input (x-value) changes.
Think of derivatives as the "speedometer" of a function. Just like a speedometer tells you how fast you're going at any given moment, derivatives tell you how fast a function is changing at any specific point.
Tangent Line: A tangent line is a straight line that touches a curve at only one point and has the same slope as the curve at that point.
Rate of Change: Rate of change refers to how quickly one quantity changes in relation to another quantity.
Instantaneous Velocity: Instantaneous velocity is the derivative of position with respect to time. It represents an object's velocity at an exact moment in time.
AP Calculus AB/BC - 1.1 Introducing Calculus: Can Change Occur at An Instant?
AP Calculus AB/BC - 1.7 Selecting Procedures for Determining Limits
AP Calculus AB/BC - 2.2 Defining the Derivative of a Function and Using Derivative Notation
AP Calculus AB/BC - 2.7 Derivatives of cos x, sinx, e^x, and ln x
AP Calculus AB/BC - 2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
AP Calculus AB/BC - 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration
AP Calculus AB/BC - 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled
AP Calculus AB/BC - 9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions
How can technology such as a calculator or software be used to estimate derivatives?
Why is estimating derivatives an important concept in Calculus?
What notation is commonly used for derivatives in implicit differentiation?
How can we find the derivatives of inverse trigonometric functions?
What kind of problems can derivatives be helpful for?
What is the relationship between L'Hôpital's Rule and derivatives?
How can relative extrema be identified by analyzing the derivatives of a function?
The motion of a rolling ball on the coordinate plane is given by the set of parametric equations x(t) = 12sin(t) and y(t) = 6t^2. Which of the following derivatives is incorrect?
Study guides for the entire semester
200k practice questions
Glossary of 50k key terms - memorize important vocab
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.