Determine the derivative of `-7 / (2x^2-8x+16)`

Expert Answers
justaguide eNotes educator| Certified Educator

The derivative of f(x) = `-7/(2x^2-8x+16)` has to be determined. Use the quotient rule.

f'(x) = `((-7)'*(2x^2-8x+16) - (-7)*(2x^2-8x+16)')/(2x^2-8x+16)^2`

=> `(7*(4x - 8))/(2x^2-8x+16)^2`

=> `(7*(x - 2))/(x^2-4x+8)^2`

=> `(7x - 14)/(x^2-4x+8)^2`

The derivative of `-7/(2x^2-8x+16)` is `(7x - 14)/(x^2-4x+8)^2`

zslady1 | Student

Thank you very much! Super helpful :)

zslady1 | Student

Actually, sorry, I do have a question.

I'm not sure what happened after this step:


f'(x) =


Where did the (2x^2-8x+16) go in the first part of the product rule? How does it cancel out?...this is the only confusion I'm having with the question.


Thank you again :)