*Presenter: Martin Lindsay (M)
M:	Hi, I’m Martin Lindsay from the Study and Learning Centre at RMIT University. This is a short movie on the product rule.

The product rule is used when we want to differentiate the product of two functions. So, if f of x, is equal to u of x times v of x, then the derivative f dash x is u of x times v dash x plus u dash x times vx. This formula can be abbreviated to y dash is equal to u times v dash, plus v times u dash. Note also that f dash x and y dash mean the same thing. 

So lets do a couple of examples to illustrate the product rule. Here’s a function, x plus 3 to the power of six multiplied by 2x minus 1. Notice here that there are two functions so we can use the product rule. So, let u equal x plus 3 to the power of 6, therefore the derivative is u dash equals 6 brackets x plus 3 to the power of five and let v equals 2x minus 1, and the derivative there is v dash equals 2. Notice I’ve used the chain rule to work out u dash. Substituting in to the formula y dash equals uv dash plus vu dash I get the following four lines of working. Notice when you get down to the third line that I’ve taken a factor of 2 brackets x plus 3 to the power of 5 out, and in the last line I’ve simplified the expression inside the square brackets to give us an answer of 14x brackets x plus 3 all to the power of 5.

Here’s another example. Again notice that there are two functions here e to the x multiplied by sin of 2x. So, this lends itself to the product rule. So I’m letting u equals e to the x, the derivative is the same e to the x and v equals sin of 2 x from which the derivative is 2 cos of 2 x using the chain rule. Substituting as before into the formula y dash equals uv dash plus vu dash I get the following three lines of working. Notice again always look for terms that will factorise and I’ve done that in the last line. So my answer is y dash is equal to ex brackets 2 cos 2x plus sin of 2 x.

Now try some questions for yourself. The answers to these questions are on the next slide. Thanks for watching this short movie.