Calc03-1 - 3.1 Derivatives 4-1 5 2 8 0 0 U 2 lim h 0 f(a h...

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3.1 Derivatives
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4 -1 5 2 8 0 -∞ ,0 ( ] U 2,¥ [ )
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( 29 ( 29 0 lim h f a h f a h ® + - is called the derivative of at . f a We write: ( 29 ( 29 ( 29 0 lim h f x h f x f x h ® + - ¢ = “The derivative of f with respect to x is …” There are many ways to write the derivative of ( 29 y f x =
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( 29 f x ¢ “f prime x” or “the derivative of f with respect to x” y “y prime” dy dx “dee why dee ecks” or “the derivative of y with respect to x” df dx “dee eff dee ecks” or “the derivative of f with respect to x” ( 29 d f x dx “dee dee ecks uv eff uv ecks” or “the derivative of f of x” ( of of ) d dx f x
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dx does not mean d times x ! dy does not mean d times y !
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dy dx does not mean ! dy dx ÷ (except when it is convenient to think of it as division.) df dx does not mean ! df dx ÷ (except when it is convenient to think of it as division.)
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( 29 d f x dx does not mean times ! d
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Calc03-1 - 3.1 Derivatives 4-1 5 2 8 0 0 U 2 lim h 0 f(a h...

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