Tutorial 1------- Introduction to Derive5

Introduction to Derive= (123 b) =

“Derive” is a Windows-based mathematics symbolic editor, that is, it produces mathematical symbols and allows the users to manipulate the symbols on screen. Th= ere are many such software in the market and Derive is inexpensive and easy to learn. You may download a tri= al version by googling Derive 5.The purposes of introducing you to the software are:

* to be able to write formulas correctly

* to know a symbolic software

* to help you do homework

The interface of Derive is the standard Window drop-down-menu point= and click . It opens with a blank= algebra window for manipulating formulas. (The other two types of windows, are = the

2D, and 3D-graphing windows.) . We enter formulas in the algebra wi= ndow and manipulate them. In this tutorial, the formula you need to enter using keyboard are unerlined, the window selections are written in Bold face, what is shown by Der= ive are written in Italic Bold face.

Open Derive: Click on Derive icon and we get a blank algebra window= .

Click-to-place the curser in the formula-box (at the bottom of the page) and enter

(x^2+1)(x-2)(2x-3)^2. (Use the ^ from the keyboard, ie. Shift-6, not the graphic one from the formula box.) Press OK, the screen displa= ys the input #1. (x² + 1)(x ‑ 2)(2x ‑ 3)² It is shaded indicating this is the selected expression that we are working with currently.

Click Simplify–>Expand and press Expand, we = got #2 (shaded), the expanded form of #1.

Click Simplify–>Factor and press Factor, we = got #3, back to the factored form.

Click on the (2x ‑ 3)² in #3 so only (2x ‑ 3= )² is shaded, then click Simplify–>Expand press Expand.= We have #4, with (2x ‑ 3)² expanded, but not the other factors. Hence we can access individual part of the formula. Experiment with it by clicking to see what you may select.

Click and shade 4x² - 12x + 9 in #4, press Ctr-c to copy it, place the curser in the formula box then press the= Ctr-v to paste it. The selected part is copied into the formula box. Press OK<= /b>, we get #5: 4x² - 12x + 9. The Window’s ctr-c and= ctr-v may be used to copy and paste.

Clear the formula box and enter #1 – 6*#5, press OK= . We get formla in #1 minus 6 times the formula in #6. Hence we may access= the formulas via the line numbers.

Clear the formula box and enter #1/#5, press OK. We g= et line #7, the quotient of #1 and #5. Shaded #7, select Simp= lify–>Basic, press OK. We obtai= n the reduced form of #7.

Clear the formula box and enter 1/x+1/(x+2), press OK= . Select Simplify–>Basic= , press OK. We obtain the one = block fractional form of the input . Select Simplify–>Expand, press OK. We are back to the expanded form.

Select File–>Save as, name it as myfil= e and the extension .mth is tagged automatically. Remember where you saved it. Exit Derive. Open Derive = again, Select File–>Open, find myfile.d= fw and retrieve it.

To summarize: we input formula via the formula box at the bottom.

We may keep click-and-shading portion of a formula to select= ed specific part that we wish to work with.

When entering formulas, we may use the ctr-c and ctr-v to cut and p= aste existing formulas.

We may also make new formulas with line #s.

Formulas can be expanded, factored, or simplified basically . (End of the tutorial)=

Extra credit. (10pt. 3/31):

You need to hand in written solution showing all the steps and a printout of the solution using Derive (or any other computer algebra software). The first line of the print out sh= ould be your name, entered as a comment — i.e. as “ your name”. Furthermore, ind= icate on the written solution the corresponding line number for the answer on the Derive printout.

A. Enter the following formulas so they appear in Derive exactly as they are shown here.&nbs= p;

a.        =             &nb= sp;   b.        =             &nb= sp;            =            c.        =            = e        =             &nb= sp; f

B. Expand and simplify:

a. (2x–3)(x+1) – (x –1)(x–3)        =              b. (x–3)(2x̵= 1;1) – (x –1)(2x+1)        =

c. (x–2)(3x–1) – (x +1)(2x–3)        =             d. (4x–3)(x̵= 1;1) – (2x –3)(x–3)        =            =

C. = Factor than simplify

E. Do all the following problems on paper. ( Der= ive 5 will give you the answer also)

D. Simplify

Frank Ma F/2002