`f(x) = (2 - (1/x))/(x-3)` Find the derivative of the algebraic function.

Textbook Question

Chapter 2, 2.3 - Problem 33 - Calculus of a Single Variable (10th Edition, Ron Larson).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to find derivative of the function using the quotient rule:

`f'(x)= ((2 - 1/x)'*(x - 3)- (2 - 1/x)*(x-3)')/((x-3)^2)`

`f'(x)= ((x-3)/(x^2) - 2 + 1/x)/((x-3)^2)`

`f'(x)= (x - 3 - 2x^2 + x)/(x^2(x-3)^2)`

`f'(x)= (-2x^2 + 2x - 3)/(x^2(x-3)^2)`

Hence, evaluating the derivative of the function, yields `f'(x)= (-2x^2 + 2x - 3)/(x^2(x-3)^2).`

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