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Differentiation Teacher Resources
Find teacher approved Differentiation educational resource ideas and activities
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Are your calculus pupils aware that they are standing on the shoulders of giants? This lesson provides a big picture view of the connection between differential and integral calculus and throws in a bit of history, as well. Note: The calculus controversy paper is not included but one can find a number of good resources on the Internet regarding the development of calculus and the role of Newton and Leibnez.
This video covers the differential notation dy/dx and generalizes the rule for finding the derivative of any polynomial. It also extends the notion of the derivatives covered in the Khan Academy videos, �Calculus Derivatives 2� and �Calculus Derivatives 2.5 (HD).� Note: Additional practice using the power rule for differentiating polynomials (including some with negative exponents) is available to the listener.
This video is the 4th in a series of videos that explains derivatives. First, Sal shows another example of differentiating a polynomial and then shows two examples using the chain rule. Sal continues the chain rule in the next video.
This video continues with examples of differentiating functions using the chain rule including examples that use negative exponents and more complicated nested parenthesis. Note: Additional practice on using the chain rule is available.
Sal defines the product rule and then shows two examples of how it is used. He then shows an example of finding the derivative by using both the chain rule and product rule together.
Continuing to use the chain rule, Sal shows more examples of finding the derivative, this time, by looking at composite functions. Note: The current set of practice problems titled �Chain rule 1� cannot be solved until one knows how to find the derivative of ex and trigonometric functions
In the first example, instead of actually using the quotient rule, Sal rewrites the denominator as a negative exponent and uses the product rule. In subsequent examples, Sal shows, but does not prove, the derivative of several interesting functions including ex, ln x, sin x, cos x, and tan x.
Twelfth graders investigate differentiation. In this calculus lesson plan students explore estimated and exact results for derivatives, tangent lines, implicit differentiation, and symbolic differentiation. The lesson plan provides examples with solutions and practice problems.
After defining L�Hopital�s rule, Sal shows an example of using the rule to solve for the limit as x approaches 0 of (sin x) / x. He also describes what it means for a fraction to have indeterminate form.
After applying L�Hopitals Rule once and showing that the limit is still indeterminate, Sal applies the rule a second and third time before arriving at a limit that exists. He then shows that given that the final limit exits, so do the previous ones including the limit of the first original problem. Note: Practice problems on L�Hopital�s rule are available and can be practiced now or after watching the other example videos.