d/dx [f(x)/g(x)] =
quotient rule
Using the quotient rule of differentiation, we can find the derivative of the function f(x)/g(x) with respect to x as follows:
d/dx [f(x)/g(x)] = [g(x)*(d/dx)(f(x)) – f(x)*(d/dx)(g(x))] / [g(x)]^2
= [g(x)*f'(x) – f(x)*g'(x)] / [g(x)]^2
Therefore, the derivative of the function f(x)/g(x) with respect to x is given by:
d/dx [f(x)/g(x)] = [g(x)*f'(x) – f(x)*g'(x)] / [g(x)]^2
Note that if g(x) = 0 for some value of x, the derivative is undefined.
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