# `f(x) = x^2 - 5, c = 3` Use the alternate form of the derivative to find the derivative at x = c (if it exists)

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Using the alternative definition of the derivative, the approximation of the derivative given by

`lim_(x->3)` `(f(x) -f(c))/(x-c)` = `lim_(x->3)(x^2 -5 - (3^2 -5))/(x-3)` ` `

`=(x^2 -5 -4)/(x-3) `

`=(x^2 - 9)/(x-3) `

`=((x -3)(x+3))/(x-3) `

`=(x+3) `

` ` `=(3+3) `

`=6 `

`lim_(x->2)` `(f(x)...

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