This series of videos focusing on calculus covers calculating derivatives, power rule, product and quotient rules, chain rule, implicit differentiation, derivatives of common functions.

You can take the derivatives of f(x) and g(x), but what about f(g(x)) or g(f(x))? The chain rule gives us this ability. Because most complex and hairy functions can be thought of the composition of several simpler ones (ones that you can find derivatives of), you'll be able to take the derivative of almost any function after this tutorial. Just imagine.

Discover what magic we can derive when we take a derivative, which is the slope of the tangent line at any point on a curve.

The topic that is now known as "calculus" was really called "the calculus of differentials" when first devised by Newton (and Leibniz) roughly four hundred years ago. To Newton, differentials were infinitely small "changes" in numbers that previous mathematics didn't know what to do with. Think this has no relevence to you? Well how would you figure out how fast something is going *right* at this moment (you'd have to figure out the very, very small change in distance over an infinitely small change in time)? This tutorial gives a gentle introduction to the world of Newton and Leibniz.

We told you about the derivatives of many functions, but you might want proof that what we told you is actually true. That's what this tutorial tries to do!

CK-12 Calculus Teacher's Edition covers tips, common errors, enrichment, differentiated instruction and problem solving for teaching CK-12 Calculus Student Edition. The solution guide is available upon request.

Working with large datasets that support exploration of patterns is an essential first step in becoming fluent with data. In this dynamic data science activity, students can access part of the U.S. Census Bureau’s American Community Survey, containing demographic information about California residents (e.g., marital status, sex, place of birth, employment status, and health information). Students can try some of the suggested data science challenges, such as finding out the average income of Californians of different age groups in 2013, then engage in investigating their own questions.

This problem involves the meaning of numbers found on labels. When the level of accuracy is not given we need to make assumptions based on how the information is reported. The goal of the task is to stimulate a conversation about rounding and about how to record numbers with an appropriate level of accuracy, tying in directly to the standard N-Q.3. It is therefore better suited for instruction than for assessment purposes.

Spreadsheets Across the Curriculum module. Students build a spreadsheet to find the combination of mini-pizzas and calzones that maximizes revenue given constraints on labor time and baking time.

Students apply their knowledge of linear regression and design to solve a real-world challenge to create a better packing solution for shipping cell phones. They use different materials, such as cardboard, fabric, plastic, and rubber bands to create new “composite material” packaging containers. Teams each create four prototypes made of the same materials and constructed in the same way, with the only difference being their weights, so each one is fabricated with a different amount of material. They test the three heavier prototype packages by dropping them from different heights to see how well they protect a piece of glass inside (similar in size to iPhone 6). Then students use linear regression to predict from what height they can drop the fourth/final prototype of known mass without the “phone” breaking. Success is not breaking the glass but not underestimating the height by too much either, which means using math to accurately predict the optimum drop height.

This lesson will help students master Algebra I standard 15: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations [A-CED4]. The lesson will make the connection between isolating a guilty person in a "who-dun-it" with isolating a given variable in an equation. In addition, this lesson will involve students creating a list of procedures to use when solving for a given variable. At this time it is not necessary for students to know the formal names for the properties. It is important for students to understand the concepts and take part in creating a set of procedures for isolating a variable and solving equations. This lesson results from the ALEX Resource Gap Project.

This math example explains what celestial objects a person can see with the unaided eye from the vantage points of Earth and Mars, using simple math, algebra and astronomical distance information. This resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.

The purpose of this task is to give students practice constructing functions that represent a quantity of interest in a context, and then interpreting features of the function in the light of that context. It can be used as either an assessment or a teaching task.

The primary purpose of this task is to lead students to a numerical and graphical understanding of the behavior of a rational function near a vertical asymptote, in terms of the expression defining the function. The canoe context focuses attention on the variables as numbers, rather than as abstract symbols.

The purpose of this task is to use finite geometric series to investigate an amazing mathematical object that might inspire students' curiosity. The Cantor Set is an example of a fractal.

The task requires the student to use logarithms to solve an exponential equation in the realistic context of carbon dating, important in archaeology and geology, among other places. Students should be guided to recognize the use of the natural logarithm when the exponential function has the given base of e, as in this problem. Note that the purpose of this task is algebraic in nature -- closely related tasks exist which approach similar problems from numerical or graphical stances.

In the task "Carbon 14 Dating'' the amount of Carbon 14 in a preserved plant is studied as time passes after the plant has died. In practice, however, scientists wish to determine when the plant died and, as this task shows, this is not possible with a simple measurement of the amount of Carbon 14 remaining in the preserved plant. The equation for the amount of Carbon 14 remaining in the preserved plant is in many ways simpler here, using 12 as a base.

This problem introduces the method used by scientists to date certain organic material. It is based not on the amount of the Carbon 14 isotope remaining in the sample but rather on the ratio of Carbon 14 to Carbon 12. This ratio decreases, hypothetically, at a constant exponential rate as soon as the organic material has ceased to absorb Carbon 14, that is, as soon as it dies. This problem is intended for instructional purposes only. It provides an interesting and important example of mathematical modeling with an exponential function.

This exploratory task requires the student to use a property of exponential functions in order to estimate how much Carbon 14 remains in a preserved plant after different amounts of time.

This task lets students explore the concept of independence of events. There are two alternative ways of solving the problem.