Calculus Differentiation Teacher Resources
Find Calculus Differentiation educational ideas and activities
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Calculus for electric circuits
In this circuits activity students complete a series of questions on equations, robotics and integration. There is an answer sheet.
Passive Integrator and Differentiator Circuits
In 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.
Linear Computational Circuitry
In this electrical worksheet, students draw a schematic design circuit board to grasp the understanding amplification in linear circuitry before answering a series of 35 open-ended questions pertaining to a variety of linear circuitry. This worksheet is printable and there are on-line answers to the questions. An understanding of calculus is needed to complete these questions.
The Fundamental Theorems of Calculus
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.
The Calculus Whiz Who Owned a Box Company
Learners use the relationship between volume and surface area to construct a box out of a piece of paper that maximizes volume using a table and by using graphing and calculus techniques.
Differentiation of Inverse Functions
In this calculus worksheet, students solve three problems regarding the differentiation of inverse functions. Students are also asked to show that a function is one to one and to evaluate functions at a given value.
Calculus: Derivatives 3
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, ï¿½Calculus Derivatives 2ï¿½ and ï¿½Calculus Derivatives 2.5 (HD).ï¿½ Note: Additional practice using the power rule for differentiating polynomials (including some with negative exponents) is available to the listener.
Calculus: Derivative of x^(x^x)
Sal starts with an example of finding dy/dx of y = x2 and builds to showing the solution to the more complicated implicit differentiation problem of finding the derivative of y in terms of x of y = x ^ x ^ x .
Newton Leibniz and Usain Bolt
What do Usain Bolt and calculus have in common? Using Usain Bolt as an example of distance traveled over a period of time, Sal shows why you need differential calculus to answer the question of how fast something is traveling at a specific instance in time. He also touches on a bit of the history of calculus. This video would make a good introduction to a calculus class or as a start to a larger discussion about the uses of calculus today.
Calculus: Derivatives 1 (new HD version)
Sal defines the term derivative by taking the listener on a well-organized tour of slope. First, he reviews the concept of slope of a line from algebra, then extends this idea to look at the slope of the curve by first examining a secant line to the curve and then using our knowledge of limits, defining the limit as _x approaches zero to get the slope of the tangent line to the curve. Along with the video, there is an interesting practice module that models the connection between the slopes of the tangent lines and the derivative of a function.
Calculus: Derivatives 2 (new HD version)
Sal continues where he left off with the last video, ï¿½Derivatives 1,ï¿½ by looking at the equation y = x2 and examining the slope of the secant line at a specific point. He continues with defining the limit as _x approaches zero to get the slope of the tangent line (derivative to the curve) at a specific point. In the next Khan Academy video, ï¿½Derivatives 2.5,ï¿½ he will generalize this technique to find the general formula for the slope at any point.
Calculus: Derivatives 2.5 (new HD version)
By defining the formal definition of a derivative, fï¿½(x), Sal is able to find the general form of the derivate function for the example f(x) = x2. He continues to stress the importance of an intuitive understanding of derivative functions.
Calculus: Derivatives 1
Sal defines the term derivative by taking the listener on a well-organized tour of slope. First, he reviews the concept of slope of a line from algebra, then extends this idea to look at the slope of the curve by first examining a secant line to the curve and then, using our knowledge of limits, defining the limit as _x approaches zero to get the slope of the tangent line to the curve. Along with the video, there is an interesting practice problem that models the connection between the slopes of the tangent lines and the derivative of a function. Note: This video has similar content as the Khan Academy video of the same name with ï¿½(new HD version),ï¿½ however, the graphs on the HD version are clearer.
Calculus: Derivatives 2
Sal continues where he left off with the last video, ï¿½Derivatives 1,ï¿½ by looking at the equation y = x2 and examining the slope of the secant line at a specific point, and again defining the limit as _x approaches zero to get the slope of the tangent line (derivative to the curve) at a specific point. He then generalizes this technique to find the general formula for the slope at any point. Note: This video has similar content to the Khan Academy videos ï¿½Derivatives 2ï¿½ and ï¿½Derivatives 2.5ï¿½ with the ï¿½(new HD version)ï¿½ label, however, the graphs on the HD versions are clearer.
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.
Using the binomial theorem and definition of a limit, Sal shows a proof that the derivative of xn equals nxn-1.
Proof: d/dx(ln x)=1/x
Using the definition of a limit, various properties of logarithms, and a definition of e, Sal shows the proof of derivative of ln x = 1/x. Note: The video titled ï¿½Proof of Derivatives of Ln(x) and e^x,ï¿½ has a clearer explanation of this proof.
Extreme Derivative Word Problem (advanced)
Sal shows the complex solution to a challenging derivative problem about ï¿½normalinesï¿½. This is probably beyond the scope of most first year calculus students but might be an interesting problem to show how complex these problems can get. Most of the thorny computations shown utilize techniques learned in algebra, but the notation used and the multifaceted parts of the problem make it quite involved.
Using the definition of a limit, Sal proves the derivative of ï¿½x or x1/2 is equal to _ x-1/2.