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02-01-2019
Mathematics

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which of the following expressions is the definition of the derivative of f(x)=ln(x) at the point (5,ln5)

which of the following expressions is the definition of the derivative of fxlnx at the point 5ln5 class=

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AnTiMaTteR23 AnTiMaTteR23

02-01-2019

The definition of the derivative is
[tex] \frac{f(x + h) - f(x)}{h} [/tex]
as h goes to 0. So since the f is ln(x)

[tex] \frac{ln(x+h)-ln(x)}{h}[/tex]

Since it is evaluated at 5 (the point 5, ln5), it is

[tex] \frac{ln(5+h)-ln(5)}{h}[/tex]

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