Derivatives Teacher Resources
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Young scholars analyze graphs and determine their general shape. In this calculus lesson, students solve functions by taking the derivative, sketch tangent lines and estimate the slope of the line using the derivative. They graph and analyze their answers.
In this derivative functions worksheet, students solve and complete 17 various types of problems. First, they find the slope of the tangent line at a given point. Then, students find the derivative of the given functions. In addition, they find the value of the derivative of the given function at the indicate point.
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.
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 this math worksheet, students answer 7 questions having to do with graphing derivatives of functions, rectilinear motion, speed and distance.
In this derivatives worksheet, students complete a function chart by telling the type of function, the derivative, and making an illustration of the concept. They find the intervals at which a given function is increasing or decreasing. Students find the relative extrema and draw a graph of one function.
In this algebra worksheet, students team up in groups of 3 to solve 11 problems involving functions, curves, and derivatives.
In this functions worksheet, students solve and complete 11 different types of problems. First, they find the coordinates of all points on the graph of each equation where the tangents to the graph are horizontal. Then, students write the equation of line tangent to each of the equations at the indicated point.
High schoolers practice the concept of graphing associated to a function with its derivative. They define the concepts of increasing and decreasing function behavior and explore graphical and symbolic designs to show why the derivative can be used as an indicator for the behavior.
Students graph functions and their inverse. In this graphing functions and their inverse lesson, students plot a point and its' image. Students plot the exponential and logarithm functions. Students find the slope of the function and its inverse by taking the derivative.
In this derivative of a power worksheet, students compare derivatives of functions, and graph functions. This one-page worksheet contains five multi-step problems.
In this function worksheet, students use functions to identify an electron traveling along a path. They examine the velocity vector and compute the directional derivative. This two-page worksheet contains six multi-step problems.
Students derive functions given a limit. In this calculus lesson, student define the derivative of f at x=a, knowing the derivative is a point or just a number. This assignment requires students to work independently as much as possible.
Students follow detailed directions to illustrate Rolle's Theorem on their graphing calculator. In this application of derivatives worksheet, students input a given function into their graphing calculator and graph it. They then calculate and graph the derivative of the original function.
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.
Learners explore lists and determine the derivative for that list. They use regressions to discover equations.
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.
In this video, Sal takes on the challenge of proving both the derivative of ln x = 1/x and of ex = ex, showing that no circular logic is used in the proof. It contains a clearer version of both proofs shown in the videos titled, _Proof d/dx e^x = e^x” and _Proof: d/dx (ln x) = 1/x.”
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.
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 .