How do you find the derivative of $5/((x^2) + x + 1)^2$ ?

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Answer 1 · 2018-03-12T12:51:23

$f'(x) = (-10)/((x^2+x+1)^2)$

For a question like this, you must use the quotient rule...

If $f(x) = color(red)(u) /color(green)(v)$ then...

$f'(x) = (color(green)(v) color(red)(u') - color(green)(v') color(red)(u))/ color(green)(v^2)$

So for the given function

$f(x)= color(red)(5)/color(green)((x^2 +x +1)^2)$

$f'(x) = (color(green)((x^2 +x +1)^2) color(red)(0) - color(green)(2(x^2+x+1)) color(red)(5))/ color(green)((x^2 +x +1)^2)$

$=> f'(x) = (-10(x^2+x+1))/((x^2 +x +1)^2)$

$=> f'(x) = (-10)/((x^2+x+1)^2)$

How do you find the derivative of 5/((x^2) + x + 1)^25/((x^2) + x + 1)^2?