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## 3.1 Derivatives

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**Photo by Vickie Kelly, 2003**Greg Kelly, Hanford High School, Richland, Washington 3.1 Derivatives Great Sand Dunes National Monument, Colorado**We write:**There are many ways to write the derivative of is called the derivative of at . “The derivative of f with respect to x is …”**“the derivative of f with respect to x”**“f prime x” or “y prime” “the derivative of y with respect to x” or “dee why dee ecks” “the derivative of f with respect to x” or “dee eff dee ecks” “the derivative of f of x” “dee dee ecks uv eff uv ecks” or**Note:**dx does not mean d times x ! dy does not mean d times y !**does not mean !**does not mean ! Note: (except when it is convenient to think of it as division.) (except when it is convenient to think of it as division.)**does not mean times !**Note: (except when it is convenient to treat it that way.)**The derivative is the slope of the original function.**The derivative is defined at the end points of a function on a closed interval.**A function is differentiable if it has a derivative**everywhere in its domain. It must be continuous and smooth. Functions on closed intervals must have one-sided derivatives defined at the end points. p