Section 2.2

There are three types of functions you are asked to find derivatives of in this section:

1. Polynomials (Just multiply out the numerator, combine like terms, reduce the fraction, then take the limit)
2. Variations on the function 1/x (Multiply everything in the fraction by the LCD of the little denominators)
3. Variations on the square root function. (Rationalize the numerator by multiplying the numerator and denominator both by the conjugate of the numerator)

When asked to find the equation of the tangent line (homework problems 9-14), first find the derivative.  Plug in the value of a you are given for x in f ¢(x) to get the slope of the tangent line.  Plug in the value of a you are given for x in the original function f to get the y-coordinate of your point.  Then use the formula

y – y₁= m (x - x₁).

The first question on the first test will be to state the definition of "derivative."  The answer is in definition 2.2.1 in your text.  The answer I want is not just the formula in the blue box, but the entire first sentence of the definition.