Proof: d/dx(sqrt(x)) Taking Derivatives Differential Calculus

Direct and to the point (the slope at a point that is) describes this one-page proof of the derivative of the sin(x). The definition of a derivative using a limit is the first step in this sequential, algebraic, explanation of how...

Using the definition of a limit, various properties of logarithms, and a definition of e, Sal shows the proof of the derivative of ln x = 1/x. Note: The video titled "Proof of Derivatives of Ln(x) and e^x,Ó has a more straightforward...

Using a specific example, Sal shows how to find the equation of a tangent line to a given function at a specific point. Specifically, he solves the problem of finding the tangent line to the function f(x) = xex at x = 1. This problem...

One example is finding the limit as x approaches -1 of (2x+2)/(x+1), solved by simplifying the expression and then explored intuitively by looking at the left and right-hand limits. The second example of finding the limit as x approaches...

Using the binomial theorem and definition of a limit, Sal shows a proof that the derivative of xn equals nxn-1.

What do Usain Bolt and calculus have in common? Using Usain Bolt as an example of distance traveled over time, Sal shows why you need differential calculus to answer the question of how fast something is traveling at a specific time. He...

Sal begins his explanation of limits with a few basic examples and takes a more intuitive point of view before looking at a formal mathematical definition in later videos. He starts by introducing the notation for limits and describes...

Using the derivative of ln x, the chain rule, and the definition of a limit, Sal shows proof that the derivative of ex = ex. Note: The video titled "Proof of Derivatives of Ln(x) and e^x,Ó clearly explains this proof.

Graphically find the derivative of sin(x). Using the interactive, pupils graph the slope of the tangent line to the sine function. Class members use the resulting graph to determine the derivative of the sine function. They verify their...

Learners explore lists and determine the derivative for that list. They use regressions to discover equations.