find the derivative of the algebraic function. f(x)=`(x^3+5x+3)/(x^2-1)`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The derivative of `f(x) = (x^3 + 5x + 3)/(x^2 - 1)` has to be determined.

Use the quotient rule.

`f'(x) = ((x^3 + 5x + 3)'*(x^2 - 1) - (x^3 + 5x + 3)*(x^2 -1)')/(x^2 - 1)^2`

= `((3x^2 + 5)*(x^2 - 1) - (x^3 + 5x + 3)*2x)/(x^2 - 1)^2`

= `(3x^4 - 3x^2 + 5x^2 - 5 - 2x^4 - 10x^2 - 6x)/(x^2 - 1)^2`

= `(x^4 - 8x^2 - 5 - 6x)/(x^2 - 1)^2`

The derivative of `f(x) = (x^3 + 5x + 3)/(x^2 - 1)` is `f'(x) = (x^4 - 8x^2 - 5 - 6x)/(x^2 - 1)^2`

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