Understanding the Quotient Rule for Finding the Derivative of f(x)/g(x)

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

To find the derivative of f(x)/g(x) with respect to x, we can use the quotient rule

To find the derivative of f(x)/g(x) with respect to x, we can use the quotient rule.

The quotient rule states that for two functions u(x) and v(x), the derivative of their quotient u(x)/v(x) is given by:

d/dx [u(x)/v(x)] = (v(x) * u'(x) – u(x) * v'(x)) / (v(x))^2

Applying the quotient rule to the function f(x)/g(x), we get:

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

So the derivative of f(x)/g(x) with respect to x is given by (g(x) * f'(x) – f(x) * g'(x)) / (g(x))^2.

This derivative can be useful for finding rates of change in various functions or solving optimization problems.

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