d/dx [f(x)/g(x)]
(g(x)f'(x)-f(x)g'(x))/g(x)^2 (quotient rule)
To find the derivative of f(x)/g(x) with respect to x, we can use the quotient rule of differentiation which states that:
d/dx [f(x)/g(x)] = [g(x) * d/dx (f(x))] – [f(x) * d/dx (g(x))] / [g(x)]^2
So, applying the quotient rule to the given function, we get:
d/dx [f(x)/g(x)] = [(g(x) * d/dx (f(x))) – (f(x) * d/dx (g(x))))] / [g(x)]^2
Therefore, the derivative of f(x)/g(x) with respect to x is [(g(x) * d/dx (f(x))) – (f(x) * d/dx (g(x))))] / [g(x)]^2.
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