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A simple differential algorithm is done by reducing each exponent by 1.
Do you wish to do more than this? Do you wish to plot a graph of the equation?
You'll need to add a keyboard (or some device) so that a user can type in an equation. You'll need a display.
If someone were to type in an equation, can you devise an algorithm to recognize the difference between constants and variables, coefficients and exponents? And then to perform mathematical calculations on the equation?
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There is an electronic counterpart which performs differentiation on a changing voltage: a capacitor in series. When values are chosen properly, it can indicate direction of change and its slope.
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