The quotient rule proof can be quite tedious if we are only allowed to use the definition of the derivative. In this post, this presents an *alternative way of proving the quotient rule if we are allowed to use the product rule*.

The Quotient Rule:

Let be the quotient of differentiable functions. Then, we can rearrange so that we have

Assuming that is differentiable, we can use the product rule on , which yields

Then we isolate on one side of the equation.

Now, we substitute .

We have arrived at the desired result, and this completes our proof.

## No comments

Comments feed for this article

Trackback link: https://kohar.ca/mae-113-calculus-for-liberal-arts-winter-2018/a-second-more-elegant-proof-of-the-quotient-rule/trackback/