Derivative of Tangent Function (Investigation)

Displayed below is the graph of . The y-coordinate of the blue point = the slope of the line tangent to the graph of f at the BIG WHITE POINT. Drag this BIG WHITE POINT around to observe the graph of the derivative of function f being traced out. Without opening up another tab in your browser to look it up, feel free to take a guess as to what the derivative of this function might be. (You don't have to do this right away, but you will eventually in the questions that follow.)


Recall the trigonometric identities you've learned previously. Is there a special relationship between the tangent, sine, and cosine of an angle?


Determine the derivative of the function by applying the quotient rule to the expression you obtained in (1) above.


Rewrite the expression you obtained in (2) so that it's not written as a quotient.