Using the quotient rule for differentiation, we get:
(d/dx)[f(x)/g(x)] = [(g(x)*d/dx[f(x)]) – (f(x)*d/dx[g(x)])]/[g(x)]^2
Simplifying this expression, we obtain:
(d/dx)[f(x)/g(x)] = [g(x)*f'(x) – f(x)*g'(x)]/[g(x)]^2
Therefore, the derivative of f(x)/g(x) with respect to x is [g(x)*f'(x) – f(x)*g'(x)]/[g(x)]^2.
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