## 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.

##### More Answers:

Exploring Indeterminate Forms in Mathematics | A Comprehensive Guide to Exponential Indeterminate Forms and Techniques for Evaluating ThemUnderstanding the Limit of (sin(x))/x as x Approaches 0

Limit Calculation | (cos(x) – 1)/x as x approaches 0

Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded