Question

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

Answer 1

`(dy)/(dx)=(-10(2x+1))/(x^2+x+1)^3`

Explanation:

Quotient rule states if `f(x)=(g(x))/(h(x))`

then `(df)/(dx)=((dg)/(dx)xxh(x)-(dh)/(dx)xxg(x))/(h(x))^2`

Hence as `y=5/(x^2+x+1)^2`

`(dy)/(dx)=(0xxd/dx(x^2+x+1)^2-d/dx(x^2+x+1)^2xx5)/(x^2+x+1)^4`

= `(-2(x^2+x+1)(2x+1)xx5)/(x^2+x+1)^4=(-10(2x+1)(x^2+x+1))/(x^2+x+1)^4`

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