Product Rule Example

by Batool Akmal

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    So we?ve looked at the product rule in more than one way. We?ve looked at the product rule numerically, we?ve looked at the product rule and its definition. And we?ve also done in the exhaustive derivation of the product rule. So, let?s do one more example before we move on to the next and the final rule. Let?s have a look at these questions, y equals to x cubed, 3x squared minus 1 to the 4. First thing that we need to do, is we need to spot what kind of function this is. Firstly, you can see that we have a function x cubed and that is multiplying with another function, so there?s definitely a product rule. But the second function you will also notice is a function within a function. So we?re using more than one rule here to work out the differential. Let?s just remind ourselves of what the product rule states. So the product rule says that dy/dx is vdudx plus udvdx or you could use the dash notation which ever one you prefer. It doesn?t matter what order you put them in either, because they?re plusing so you could put udvdx first, and then vdudx next, because they?re adding, it doesn?t really make a difference. So, we?re going to split this into two, so we?re going to say this is my u function which is x cubed, and this is my v function which is 3x squared minus 1 to the power of 4. We differentiate each one of them separately, so I have du/dx which gives me 3x squared. And then I have dv/dx which gives me, remember that this is now the chain rule. So firstly, the outside function, bring the power down 4, leave everything on the inside as it is, decrease...

    About the Lecture

    The lecture Product Rule Example by Batool Akmal is from the course Quotient Rule, Chain Rule and Product Rule.

    Author of lecture Product Rule Example

     Batool Akmal

    Batool Akmal

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