The Quotient Rule: How to Find the Derivative of a Quotient of Two Functions

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

To find the derivative of the quotient of two functions, f(x)/g(x), we can use the quotient rule

To find the derivative of the quotient of two functions, f(x)/g(x), we can use the quotient rule.

The quotient rule states that if we have two functions, u(x) and v(x), being divided, then the derivative can be found using the formula:

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

In this case, f(x) is the function being divided by g(x). Therefore, u(x) = f(x) and v(x) = g(x). Applying the quotient rule, we have:

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

Note that we still need to find the derivatives of f(x) and g(x), which will depend on the specific functions being used. Once these derivatives are found, we can substitute them into the quotient rule formula to evaluate the derivative of f(x)/g(x).

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