More Chain Rule Practice (2.4 #63) The Chain rule to rescue, once again!

 We attack a sec^3 function with the Chain Rule and confirm our slope with a TI-84  We attack a sec^3 function with the Chain Rule and confirm our slope with a TI-84. The show the derivative of sec x is tan x * sec x.  Next we use the chain rule to twice to find the slope at x=0.

 Tangent Line to A Circle with the Chain Rule (2.4 #79) He we find the slope of a semi-circle using the chain rule, and check our tangent line equation with a TI-84 style calculator.

 Higher Order Derivatives (2.3 #93, 103, 115) The rate of change of the rate of change is the derivative of the derivative, aka the "Second derivative".  We we write it " f''(x)" or sometimes "d^2x/dy^2".  But there is reason to stop there.  The derivative of the second derivative is the third derivative, and so on.  We will even find an eighth derivative in this video!

 Rate of change of Area per second (2.3 #83) Here we look at the rate of change of area per second which requires us to make a function (the Area of a rectangle) and compute the rate of change of that function.  This gives us a glimpse of what Calculus "word problems" look like!

 Can Different Functions Have the Same Derivative? (2.3 # 79) Here we investigate a claim that two function have the same derivative.  We use the quotient rule to confirm it, then looking at the graph, we see why these functions might actually have the same slope.

 Quotient Rule to Find a Tangent Line with a Certain Slope (2.3 #77) After using the quotient rule to find a formula for slope, we set it to a certain slope to find when the function has that slope.  To get the equation of the line, we use the original function to find the y coordinate, and place it in the "Point-Slope" form of a linear equation: y-Y = m (x-X) where the point is (X,Y) and m is the slope.  Finally we use the calculator to check our work both graphically as well as numerically.

Check your Derivative at a Point with a Calculator (2.3 # 59) After finding a derivative at a point with the quotient rule, we check our work with a TI-84 style calculator. 

 More Quotient and Product Rule (2.3 #35, 51, 55) Here the calculus is easy, but sometimes you have to use algebra to match your answer with the answer in the back of the book.  A great skill to have so you can select a multiple choice item that expresses the answer in a slightly different form than the way you have it.... 

  Can a piece-wise function be differentiable? If it is continuous, and the slopes from the left and the right are the same, yes!