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.

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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.

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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.

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

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!

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This art history video discussion examines Robert Campin's (also called the Master of Flemalle) "Christ and the Virgin," c. 1430-35, oil and gold on panel, 11-1/4 x 17-15/16 inches / 28.6 x 45.6 cm (Philadelphia Museum of Art).

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This art history video discussion examines Robert Campin's Merode Altarpiece, tempera and oil on panel, 1425-28 (Metropolitan Museum of Art).

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This short video and interactive assessment activity is designed to teach second graders about capacity comparison problems with illustrations - word problems.

This short video and interactive assessment activity is designed to teach fourth graders about finding the amount of water with illustrations and calculations (metric units).

This short video and interactive assessment activity is designed to teach third graders an overview of capacity IIi (metric units).

This short video and interactive assessment activity is designed to teach second graders about capacity problems with illustrations - word problems.

This art history video discussion examines Caravaggio's "Calling of St. Matthew," oil on canvas, c. 1599-1600 (Contarelli Chapel, San Luigi dei Francesi, Rome).

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This art history video discussion examines Caravaggio's "Crucifixion of St. Peter", oil on canvas, 1601 (Santa Maria del Popolo, Rome).

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This art history video discussion examines Caravaggio's "Death of the Virgin," 1605-06, Oil on canvas, 12 feet, 10 inches x 8 feet (369 x 245 cm) (Musee du Louvre, Paris). Painted for the altar of a family chapel in the church of Santa Maria della Scala del Trastevere, Rome.

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This art history video discussion looks at Michelangelo Merisi da Caravaggio's "Narcissus at the Source", oil on canvas, 1597-99 (Palazzo Barbarini).

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This art history video discussion examines Michelangelo Merisi da Caravaggio's "The Supper at Emmaus", 1601, oil on canvas (National Gallery, London).

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

In this video segment adapted from NOVA, find out how cars made of a material stronger than steel and half the weight can help combat climate change.

In this video segment from NatureScene, explore Cartwheel Bay, a wetland in South Carolina, and learn about the variety of carnivorous plants native to this unique landform.

In this video adapted from Texas Parks and Wildlife Department, learn about carnivorous plants that act as both producers and consumers in an ecosystem. See sundews and blatterworts capture and digest insects.

In this episode on Building Resilient Ecosystems for Education, Dr. Caroline Levander, who views university campuses as places of passion and dynamism, will provide insight into her roles as a university leader and scholar, and discuss the nuts and bolts of building community in higher education. A new virtual interview series from LabXchange at Harvard University, The Xchange showcases the diverse roles, projects, and initiatives that make up the intersecting fields of science, education, and health. Hosted by LabXchange Faculty Director Robert Lue, our first season features a range of perspectives on the impact of COVID-19.

This art history video discussion examines Jean-Baptiste Carpeaux's "Dance," 1865-69, marble, 420 x 298 cm (Musee d'Orsay, Paris). Commissioned by Charles Garnier for the facade of L'Opera. In 1964 it was replaced by a copy executed by Paul Belmondo.

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.