Question

How do you differentiate `f(x)=(x-3)/(x^2-x+1)` using the quotient rule?

Answer 1

For a function `f(x)=(p(x))/(q(x))` the derivative is

`(d(f(x)))/dx=[(dp(x))/dx*q(x)-p(x)*(dq(x))/dx]/(q(x))^2`

Now if we apply for `p(x)=x-3` and `q(x)=x^2-x+1`

we find that

`(df(x))/dx=-[x^2-6x+2]/(x^2-x+1)^2`