Interactive
CK-12 Foundation

Differential Equations Representing Growth and Decay: Rice Legend

For Students 11th - Higher Ed
The legend of a wise man who asks a king for rice as a reward presents a context to study exponential solutions to differential equations. Pupils move quantities of rice to a chessboard and calculate the amount of rice for each day. To...
Interactive
Curated OER

Differentiation Using the Chain Rule

For Students 10th - 12th
In this calculus worksheet, students solve problems using differentiation and the chain rules. They take the derivatives of equations using specific equations. There are 21 problems with an answer key.
Interactive
Curated OER

Logarithmic Differentiation

For Students 12th
In this calculus worksheet, 12th graders perform logarithmic differentiation on functions for which the ordinary rules of differentiation do not apply.  The one page interactive worksheet contains eleven problems.  Answers are...
Interactive
Curated OER

Implicit Differentiation Problems

For Students 9th - 10th
In this calculus worksheet, students perform implicit differentiation to take the derivative. They solve function explicitly of x. They differentiate between implicitly and explicitly. There are 16 problems with an answer key.
Interactive
Curated OER

Passive Integrator and Differentiator Circuits

For Students 10th - Higher Ed
For this circuits worksheet, students answer 25 questions about passive integrator circuits and passive differentiator circuits given schematics showing voltage. Students use calculus to solve the problems.
Interactive
CK-12 Foundation

Logarithmic Differentiation: Graphing the Derivative of a Logarithm

For Students 11th - Higher Ed
Log the values of the derivative of a logarithm. The interactive plots the derivative of the natural logarithm. Learners first determine the derivative of natural logarithm and the general logarithm. Using the formulas for the...
Interactive
Curated OER

The Method of Integration by Parts

For Students 11th - 12th
In this calculus worksheet, students perform integration by parts. They solve differential equations as they use integration by part to solve unlike terms. There are 23 problems with an answer key.
Interactive
Curated OER

Product Rule

For Students 9th - 10th
In this calculus worksheet, learners find the derivative of a function. They use the product rule to to differentiate each problem. There are 21 problems with an answer key.
Interactive
Curated OER

The Method of U-Substitution

For Students 9th - 10th
In this calculus learning exercise, students solve problems using U-Substitution. They find antiderivatives  using indefinite integrals. There are 18 questions with an answer key.
Interactive
Curated OER

Word Problems

For Students 10th - 11th
In this calculus worksheet, students use integration to solve word problems they differentiate between integration and anti derivatives, and between definite and indefinite integrals. There are 3 questions with an answer key.
Interactive
CK-12 Foundation

Antiderivative: Piecing it Together

For Students 11th - Higher Ed
Build a function backwards. Given a graph of the derivative of a function, pupils piece together a graph of the original function, the antiderivative. Learners use their graphs and the graphs of the derivatives to answer questions about...
Interactive
CK-12 Foundation

Constant, Identity, and Power Rules: Power Rule

For Students 11th - Higher Ed
Learn to gain power in finding derivatives. The resource introduces the power rule. Using the sliders in the interactive, pupils create polynomial functions and find their derivatives. Given the derivative of a polynomial, learners...
Interactive
CK-12 Foundation

Chain Rule

For Students 11th - Higher Ed
Keep it on the chains. Pupils work through the steps in the chain rule using the interactive as a guide. Learners identify the two composed functions and their associated derivatives from a set of choices. They continue on to build the...
Interactive
CK-12 Foundation

Higher Order Derivatives—Acceleration and Jerk

For Students 11th - Higher Ed
Accelerate your class through finding the second derivative. Using a bank of equations, pupils determine the equations for distance, velocity, and acceleration and their associated function notations. With the equations, learners answer...
Interactive
CK-12 Foundation

Derivatives with Mean Value Theorem and Rolle's Theorem: Maxima and Minima

For Students 11th - Higher Ed
Rolle with the mean values and derivatives. Scholars complete the statements of Rolle's Theorem and the Mean Value Theorem. Using the interactive to illustrate scenarios, pupils respond to questions concerning the theorems in terms of...
Interactive
CK-12 Foundation

Slope of a Tangent Line: Slope of the Tangent and Secant Lines

For Students 11th - Higher Ed
Learn to find the slope through a single point. The interactive provides a visualization of how to find the slope of a tangent line. With the aid of the visualization, pupils see the definition of the derivative in action. Class members...
Interactive
CK-12 Foundation

Tangent Line Approximation: Estimating Square Roots

For Students 11th - Higher Ed
Estimating a square root is as easy as evaluating a linear equation. Using the derivative of the square root function, pupils calculate an estimation of square roots. Class members determine the equation of the tangent line at the value...
Interactive
CK-12 Foundation

Derivatives of Trigonometric Functions: Derivative of sin(x)

For Students 11th - Higher Ed
Graphically find the derivative of sin(x). Using the interactive, pupils graph the slope of the tangent line to the sine function. Class members use the resulting graph to determine the derivative of the sine function. They verify their...
Interactive
CK-12 Foundation

Related Rates of Car Speeds

For Students 11th - Higher Ed
Speed up your pupils' understanding of derivatives. Two cars travel in perpendicular distances to each other. With the aid of the interactive, learners visualize the situation. Pupils use the derivative to calculate the instantaneous...
Interactive
Interactive Mathematics

Interactive Mathematics: Differentiation

For Students 9th - 10th
Explore the world of Calculus through differentiation. Focusing on areas such as limits, tangents to curves, and derivatives, this site shows you how to solve problems based on the discoveries of Sir Isaac Newton and Gottfried Leibniz....