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Calculus/calculus, quotient rule


Will try not to waste time and get right to my question (thank you for taking it).

If f(x)=(2x-3)/(4x+5) (parenthesis added for clarity) find f'(x)

Sorry about the delay, but I just managed to get to this question.
If f(x) = g(x)/h(x), then f'(x) { without the (x) for each function } = [hg'-gh']/h^2.

Since g(x) = 2x-3, it is easily seen that g'(x)=2.
Since h(x) = 4x+5, it is easily seen that h'(x)=4.

Putting these into [hg'-gh']/h^2 gives [2(4x+5) - 4(2x-3)](4x+5)^2.

That is, (8x + 10 - 8x + 12)/(4x+5)^2, which reduces to 22/(4x+5)^2.


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