Derivatives of Power Functions and Polynomials

Guided Notes for this lecture

Now that we understand instantaneous rate of change we are able to find patterns of derivatives which lead us to formulas we can use to compute derivatives based on the type of function we have.

If we have a constant that multiplies our original function, that constant carries to the derivative.

If we add or subtract two functions that are polynomials or power functions, we can add or subtract their derivatives.

We can use our formulas to compute second (or third, fourth, etc) derivatives of functions. .

There are some common applications that we will see now that we know how to find the derivative in a more forulaic way. This video outlines the common examples. .

Another set of derivatives to add to our list of formulas is the sine and consine function.

At the end of this section you should be able to answer the following questions:

1. What types of functions can we apply the power rule to?
2. How do the derivative formulas relate to the tangent line?
3. What is the process to find the equation of a tangent line?

Check Your Understanding
You should try these problems before reviewing the solutions to to these non-graded practice problems.