Product and Quotient Rule

# Product and Quotient Rule - Product and Quotient Rule In...

This preview shows pages 1–3. Sign up to view the full content.

Product and Quotient Rule In the previous section we noted that we had to be careful when differentiating products or quotients. It’s now time to look at products and quotients and see why. First let’s take a look at why we have to be careful with products and quotients. Suppose that we have the two functions and . Let’s start by computing the derivative of the product of these two functions. This is easy enough to do directly. Remember that on occasion we will drop the (x) part on the functions to simplify notation somewhat. We’ve done that in the work above. Now, let’s try the following. So, we can very quickly see that. In other words, the derivative of a product is not the product of the derivatives. Using the same functions we can do the same thing for quotients.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
So, again we can see that, To differentiate products and quotients we have the Product Rule and the Quotient Rule . Product Rule If the two functions f(x) and g(x) are differentiable ( i.e. the derivative exist) then the product is differentiable and, The proof of the Product Rule is shown in the Proof of Various Derivative Formulas section of the Extras chapter. Quotient Rule If the two functions f(x) and g(x) are differentiable ( i.e. the derivative exist) then the quotient is differentiable and, Note that the numerator of the quotient rule is very similar to the product rule so be careful to not mix the two up! The proof of the Quotient Rule is shown in the Proof of Various Derivative Formulas section of the Extras chapter.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern