Quotient Rule: d/dx [ f(x) / g(x) ]
[ f'(x)g(x) – f(x)g'(x) ] / (g(x))²
The quotient rule is a differentiation rule used to find the derivative of a function that is a quotient of two other functions.
If we have f(x) and g(x) as two differentiable functions, then the quotient rule can be expressed as follows:
d/dx [f(x) / g(x)] = [ g(x) * d/dx(f(x)) – f(x) * d/dx(g(x)) ] / [ g(x) ]^2
In other words, to find the derivative of a quotient of functions, we first take the derivative of the numerator (f(x)) and multiply it by the denominator (g(x)) minus the derivative of the denominator (g(x)) multiplied by the numerator (f(x)). Then, we divide this result by the square of the denominator (g(x))^2.
It’s important to note that this rule only applies if g(x) ≠ 0 since division by zero is undefined.
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