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.)
2. 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.
3. 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.
4. Repeat the above step with the expression DIF(sin (x^2),x). Observe the
way to write exponents.
5. 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.
6. 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.
7. Try a few other derivatives. Use the Help option to look up the correct
syntax for know functions.
8. 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.
9. Enter int(2^(3x),x) into the input box and select the check/equal option.
The integral of 23x is displayed.
10. 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.
11. 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.
12. 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.
13. 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.
9
a.

1
1
x
b. lim sin x
x→0 x
x5
dx
2
x
2
7
c.

d. second derivative of (arctan(x) - arccos(3x))
e.
3
2
2
 x  4 x  2dx   x dx