DERIVE ACTIVITY 1 BORROW THE TI RESOURCE CD FROM

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DIF(sin x, x) press return

Derive Activity


  1. Borrow the TI Resource CD from SV203 and install the Derive program on your system. (It has a 30 day trial period.)


  1. Open the program and examine the page. The display area is in the center and special key options are at the bottom. The input text box is above the special key options and next to the row of checks, equal and approximation icons. The check icon will display the expression, the equal will compute it, and the combination check and equal will do both. The same thing for the approximation icons.


  1. Enter the following expressions in the input text box to find the derivative of sin x with respect to x: DIF(sin x, x) Then click on the combination check and equal icon. In the display area the first line displays the typed expression and the second line displays the result.


  1. Repeat the above step with the expression DIF(sin (x^2),x). Observe the way to write exponents.


  1. Use Derive to find the derivative of (ln x)(arctan (x2). Note: write arctan as atan and don’t forget the extra x to indicate the derivative is with respect to x.


  1. The special key ê represent the mathematical value e. Find it on the far right of the special key options and use it to use Derive to find the derivative of the expression e(csc x). Observe that the answer is in terms of sines and cosines.


  1. Try a few other derivatives. Use the Help option to look up the correct syntax for know functions.


  1. While the last derivative problem you entered is still in the input box, click on the integral icon on the toolbar at the top of the page. A window will open with some options. Select ‘Simplify.’ You have just asked Derive to that the integral of the derivative of a function. The result should be the original function.


  1. Enter int(2^(3x),x) into the input box and select the check/equal option. The integral of 23x is displayed.


  1. Enter the expression (x2 + 4)(x3 – 5) + x3 and select the equal option. Use the line number of the resulting expression


#nn: x5 + 5·x3 - 5·x2 - 20

in the expression int(#nn, x). Enter this expression in the input box and select the check/equal option. This is another way of finding an integral. Use dif(#nn,x) to find the derivative.


  1. Scroll back through the Derive output and select the expression x5 + 5·x3 - 5·x2 – 20. Then click on the sigma option on the toolbar on the top. Set the upper limit to 5 and simplify. Derive will compute the sum to be 5175.


  1. Click on any location in the output. Select the text box icon (a square with the letters AB and a picture of a pencil). This will insert a text box into which you can write comments.


  1. Experiment until you feel comfortable with the program interface and can use it to solve the following problems. Unlike some similar programs, Derive does not copy well to word files. Therefore to turn in your result, add text boxes to identify the answers and print out the Derive output. Bring the hard copy to SV203.


a. DERIVE ACTIVITY 1 BORROW THE TI RESOURCE CD FROM


b. lim sin x

x→0 x


c. DERIVE ACTIVITY 1 BORROW THE TI RESOURCE CD FROM


d. second derivative of (arctan(x) - arccos(3x))


e. DERIVE ACTIVITY 1 BORROW THE TI RESOURCE CD FROM



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