d/dx[f(x)/g(x)]=
g(x)f'(x)-f(x)g'(x)/g(x)^2
The derivative of the ratio of two functions f(x) and g(x) with respect to x is given by the quotient rule:
d/dx [f(x)/g(x)] = [g(x)*d/dx[f(x)] – f(x)*d/dx[g(x)]] / [g(x)]^2
Alternatively, you can simplify this expression by multiplying both the numerator and denominator of the original function by g(x) to obtain:
d/dx [f(x)/g(x)] = (d/dx[f(x)]*g(x) – f(x)*d/dx[g(x)]) / [g(x)]^2
Either expression can be used to calculate the derivative of a function that is expressed as the ratio of two other functions. Remember to follow the order of operations and simplify the final expression as much as possible.
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