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Q : f (x)=(5x -1)/(5x+1) f'=?

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ruals | (Level 1) Salutatorian

Posted July 5, 2013 at 4:55 PM via web

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Q : f (x)=(5x -1)/(5x+1)

f'=?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 5, 2013 at 5:13 PM (Answer #1)

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You need to differentiate the function with respect to x, using the quotient rule, such that:

`f'(x) = ((5x - 1)'(5x + 1) - (5x - 1)(5x + 1)')/((5x + 1)^2)`

`f'(x) = (5(5x + 1) - 5(5x - 1))/((5x + 1)^2)`

Factoring out 5 yields:

`f'(x) = (5(5x + 1 - 5x + 1))/((5x + 1)^2)`

Reducing duplicate members to numerator yields:

`f'(x) = 10/((5x + 1)^2)`

Hence, evaluating the derivative of the given function, using the quotient rule, yields `f'(x) = 10/((5x + 1)^2).`

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