| The Power Rule |
What is the question that I will be asked which requires me to do the power rule?
What is the general formula for doing the power rule?
What are the steps for doing the power rule?
What is the appropriate notation?
What is the type of question that I will be asked that requires
me to do the power rule?
Directions: Please calculate the derivative for the following function.
f(x)=8x5-5x-4+x-2
What is the general formula for doing the power rule?
When given a polynomial function whose terms are of the form
You do the following for each term.
What are the steps for doing the power rule?
| Steps | Example |
| 1. Make sure every term of the given polynomial function is written of the form axn. (I.e. make sure there are no variables in the denominator.) | f(x)=x7-8x5+20x-2 |
| 2. For each term, take the exponent (n) and multiply it by the coefficient (a). Then decrease the exponent by one. | f'(x)=(1·7)x7-1-(8·5)x5-1+(20·(-2))x-2-1 |
3. Simplify the new polynomial expression and check that your notation is correct. |
f'(x)=7x6-40x4-40x-3 |
What is the appropriate notation?
| Given Function | Notation for the Derivative |
| f(x)=... (read f of x) | f'(x)=...(read f prime of x) |
| g(x)=... | g'(x)=... |
| h(x)=... | h'(x)=... |
| y=... | y'=... |