We want to determine the derivative of the given function f of x equals two x squared times e to the power of five x. So we need to recognize here that we have a product of two functions. The first function we’ll let equal two x squared, and the second function will be e to the power of five x. So we'll let f equal two x squared and then we'll let g equal e to the power of five x. Now we'll set up the product rule given here. So f prime of x is going to be equal to f times g prime plus g times f prime, or the first function two x squared times the derivative of e to the power of five x plus the second function e to the power of five x times the derivative of the first function two x squared. Now notice how I didn't determine any derivatives yet; I just set this up. So now we'll go back and determine this derivative here and this derivative here. Well, for the derivative of e to the power of five x, this is a composite function, so we'll let u equal five x. The derivative of e to the power of u is going to be e to the power of u times u prime, so we'll have e to the power of five x times five. Plus, e to the power of five x times the derivative of two x squared, which would be four x. So let's go ahead and determine these products here. We'll have ten x squared e to the power of five x plus here we'll have four x times e to the power of five x. On these types of problems, you'll normally see the final derivative in factored form. So the greatest common factor would have a factor of two, a factor of x, and a factor of e to the power of five x. So if we factor out two x e to the power of five x, let's see what's left. We’d have a factor of five x left here, and we’d have a factor of two here. So when we apply the product rule like this, I think it is helpful to show this step here and then determine the derivatives in the next step. We’ll take a look at an example that involves the exponential function and the quotient rule in the next video.