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This Exploration demonstrates how to find the symbolic derivative of a function using X(PLORE), a shareware programme downloadable from David Meredith in both DOS and Windows® versions. It does algebraic manipulation, symbolic calculus and lots more. (Disclaimer: While I have had no difficulties using this program, please undestand that you use it at your own risk.)
Instructions
If you haven't already done so, download and install X(PLORE). Run X(PLORE) and minimise the window. In this Activity, you will switch between this page and X(PLORE), by minimising and maximising the X(PLORE) window. Follow the instructions below.
- Finding the derivative of a function
To find the the derivative of f(x) = cos (2x - 1):
- Firstly, we define the function. Where the cursor is flashing type
f(x) = cos (2*x - 1)
and then press the "Enter" key on the keyboard.
- Next, we sketch the function to ensure that it is continuous over the required bounds. Where the cursor is flashing on the new line type
Sketch (f(x), x = -2 to 2)
and press the "Enter" key.
- Now we find the required derivative. Where the cursor is flashing type
e = Dif(f(x) , x)
and press the "Enter" key.
- Alternatively we can avoid defining the function and just enter the command:
e = Dif(cos (2*x - 1) , x)
and press the "Enter" key.
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