How do you use the definition of a derivative to find the derivative of $f(x) = 3/(x-2)$ to calculate f'(a)?

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Answer 1 · 2017-09-26T20:38:47

$f'(a) = -3/(a-2)^2$

By definition of derivative:

$f'(a) = lim_(x->a) (1/(x-a))(3/(x-2)-3/(a-2))$

$f'(a) = lim_(x->a) (1/(x-a))(3(a-2)-3(x-2))/((a-2)(x-2))$

$f'(a) = lim_(x->a) (1/(x-a))(3a-6-3x+6)/((a-2)(x-2))$

$f'(a) = lim_(x->a) (1/(x-a))(-3(x-a))/((a-2)(x-2))$

$f'(a) = lim_(x->a) -3/((a-2)(x-2))$

$f'(a) = -3/(a-2)^2$

How do you use the definition of a derivative to find the derivative of f(x) = 3/(x-2)f(x) = 3/(x-2) to calculate f'(a)?