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1. By choosing COMP from the main menu and pressing [SHIFT] [d/dx] a numerical derivative facility can be accessed.

For example, d/dx(x²,3,1E-3) will give the value of the derivative of y = x² with respect to x, at x = 3; namely 6.

2. The d/dx( facility can be used in a graphing expression. For example, in the screen below, Y2 is the derivative of Y1 = A^x. (Note, Y1 is accessed through the [SHIFT] [VAR] [F1] [F1] key sequence). ‘A’ is a constant with respect to the differentiation. The second parameter, X, indicates that the derivative will be evaluated at each value of X.

3. You are going to investigate the power function, y = a^x and try to discover the unique function whose derivative is identical to itself. As a start, set up the range and the initial value of A as follows:

4. The graph of y = 2^x and its derivative are shown below. The two curves are similar; in fact, dy/dx = k2^x. Confirm , using the [TRACE] facility, that k is approximately 0.7.

5. The graphs below are those for y = 3^x. Confirm that k is approximately 1.1.

6. By changing A, find its value so that the derivative is identical to the function. In other words, find A so that k = 1.

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