Find the derivative of (x+3)/(2x-5)

We have to find the derivative of
(x+3)/(2x-5).

This can be done using the product rule which
states that the derivative of h(x) = f(x)* g(x) = f'(x)*g(x) + f(x)*g'(x) and the chain
rule

Take the given expression
(x+3)/(2x-5)

= (x+3)*(2x -
5)^-1

The derivative is (x +3)*(-1)*2*(2x - 5)^-2 + 1*(2x -
5)^-1

=> -2(x + 3)/ (2x - 5)^2 + 1/ (2x -
5)

=> [-2x - 6 + 2x - 5]/ (2x -
5)^2

=> -11 / (2x -
5)^2

The required result is -11 / (2x -
5)^2