Differentiation Quotient Rule

The quotient rule applies when you have a fraction with a function in the numerator, and a function in the denominator such as f(x) / g(x). Providing each function has a derivative, simply substitute the values into the quotient rule formula for the answer.

The best way to work with this formula is to first find the derivative of g(x), derivative of f(x), and also [g(x)]². Then it is a simple matter of substituting them into the formula. If you work with small sections of the formula in this way then it becomes an easy task.

Quotient Rule Example

Here is a simple fraction type function y = (x+1)/x, which solves in many different ways.

The top part of the fraction becomes a function given by f(x) = x+1, whilst the bottom part becomes another function given by g(x) = x. Hence, the fraction is f(x)/g(x).

Differentiating x+1 results in a derivative with a value of 1.

Differentiating x results in a derivative with a value of 1.

All that remains now is to substitute the values into the quotient formula shown at the top of this page.

This is how it simplifies.

Finally, the answer is -1/x².

This Article Continues...