How To Use The Quotient Rule Of Differentiation For Finding Derivatives Of F(X) / G(X)

d/dx [f(x)/g(x)]

(f'(x)g(x)-f(x)g'(x)) / (g(x))^2

To differentiate [f(x) / g(x)], we’ll need to use the quotient rule of differentiation.

According to the quotient rule, the derivative of [f(x) / g(x)] is equal to:

[(g(x) * d/dx[f(x)]) – (f(x) * d/dx[g(x)])] / [g(x)]^2

So, we need to find the first derivatives of f(x) and g(x) with respect to x:

d/dx[f(x)] and d/dx[g(x)]

Let’s use f'(x) to represent d/dx[f(x)] and g'(x) to represent d/dx[g(x)], so we don’t have to keep writing out the derivative notation.

Using the quotient rule, the derivative of [f(x) / g(x)] is:

[f'(x) * g(x) – f(x) * g'(x)] / [g(x)]^2

So, the final answer is:

d/dx[f(x) / g(x)] = [f'(x) * g(x) – f(x) * g'(x)] / [g(x)]^2

In other words, we multiply the derivative of the numerator with the denominator, subtract the numerator times the derivative of the denominator from it and then divide the whole thing by the square of the denominator.

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