Differentiate the function f(x)= (2x-3)/(x^2-5)

Given that f(x)= (
2x-3)/(x^2-5)

We need to find the first derivative
f'(x)

We will use the porduct rule
.

Let f(x)= u/v such that:L

u=
2x-3  ==> u' = 2

v= x^2 -5 ==> v' =
2x

Then we know that:

f'(x)= (
u'v - uv')/v^2

==> f'(x)= ( 2(x^2-5) - 2x(2x-3) /
(x^2-5)^2

==> f'(x)= ( 2x^2 -10 - 4x^2 +
6x)/(x^2-5)^2

==> f'(x)= ( -2x^2 + 6x
-10)/(x^2-5)^2

==> f'(x)= -2(x^2 -3x
+5)/ (x^2-5)^2