How do I differentiate something in the form f(x)/g(x)?

To differentiate the quotient of two functions f(x)/g(x) you can use the quotient rule, the formula of which is: (f'(x)*g(x)-f(x)*g'(x))/g²(x)

it is important to remember which part you have to differentiate first: let's pick our f(x)/g(x) again

the trick I used was thinking that in the derivative the denominator has to be squared (g²(x)), so it gets "tired". Therefore, in the first part of our numerator, f(x) will be derived while g(x) rests and remains the same, and to that we will subtract f(x) multiplied by the derivative of g(x)