Calculus 2
Calculus 1 Name ____________________________ Power Rule Notes
Derivatives – Slope of a Tangent
The expression found when determining the expression for the slope of a tangent ([pic]) for a function is called the derivative of the function. The derivative is used to find the instantaneous rate of change for any value of the independent variable. The various symbols for the derivative are:
[pic].
The following are examples of several functions and their respective derivatives.
1) [pic] 2) [pic] 3) [pic]
4) [pic] 5) [pic] 6) [pic]
Using the six examples from above and without using the Limit Definition of the Slope of a Tangent Line, establish some short-cut rules for finding derivatives of functions. Use these rules to find the derivatives (the expression for the slope of a tangent) of the following functions:
a) [pic] b) [pic] c) [pic]
d) [pic] e) [pic] f) [pic]
g) [pic] h) [pic] i) [pic]
*This short-cut is called the Power Rule
Power Rule
Sometimes you have to change the look of the function to be in the right form to take the derivative using the short-cut.
j) [pic] k) [pic] l) [pic]
m) [pic] n) [pic] o) [pic]
Determine the equation of the tangent line of [pic]at x = 0.
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