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# AP Calculus AB

An interactive log for students and parents in my AP Calculus class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

## Tuesday, November 08, 2005

### Suddenly Not So Ugly

Today in class, we started the fourth unit, and yet again the derivative function shows itself once again. We learned how to convert a parent function into a derivative function without using the Definition of the Derivative Function.

If the parent function is a constant function, for example: f (x) = 2
The derivative function is automatically zero (0), f ' (x) = 0

If the parent function is a linear function, for example: f (x) = 2x
The derivative function is the slope of the line (m), f ' (x) = 2

If the parent function is a power, for example: f(x) = x^3
To convert from the parent function to the derivative function by taking the exponent and make it the coefficient, then subtract 1 from the exponent to get the derivative function.

f (x) = x^n
f ' (x) = n(x^(n-1))

Now with these short cuts the derivative function is not as ugly as it once was.

The next scribe is Ara.