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3.1 Derivatives Great Sand Dunes National Monument, Colorado Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003

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is called the derivative of at. We write: The derivative of f with respect to x is … There are many ways to write the derivative of

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f prime xor the derivative of f with respect to x y prime dee why dee ecks or the derivative of y with respect to x dee eff dee ecks or the derivative of f with respect to x dee dee ecks uv eff uv ecksor the derivative of f of x

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dx does not mean d times x ! dy does not mean d times y !

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does not mean ! (except when it is convenient to think of it as division.) does not mean ! (except when it is convenient to think of it as division.)

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(except when it is convenient to treat it that way.) does not mean times !

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In the future, all will become clear.

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The derivative is the slope of the original function. The derivative is defined at the end points of a function on a closed interval.

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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.

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