By: Jenn Gulya

The derivative of a function f with respect to the variable is the function f ‘ whose value at x, if the limit exists, is: This value is, also, representative of the slope of the function at a point.

Where a is an x value, F(a) must be differentiable for f’(a) to exist. So at some points a derivative may not exist. (An example would be the absolute value graph, which lacks a derivative at x=0).

1. Derivative of a Constant Function: If f is the function with a constant value c, then f’ = 0 2. Power Rule for Positive/ Negative Integer Powers of x: If n is a positive/negative integer, then

3. The Constant Multiple Rule If u is a differentiable function of x and c is a constant, then 4. The Sum and Difference Rule If u and v are differentiable function of x, then their sum and difference are differentiable at every point where u and v are differentiable. At such point

Y= x 3 +6x 2 -(5/3)x+16 Applying Rules 1 through 4, differentiate the polynomial term-by-term

Graph of original Function: Graph of derivative: It can be seen that when the original curve levels off and changes direction the graph of f’ crosses the x-axis.

Calculations can be graphically supported. Differentiate f(x)=

When the calculated derivative and NDER of the function on the calculator are graphed together. They appear to be identical, which is a strong indication that the calculation is correct.

Will be majoring in Biology at Rutgers University in the Fall.