And then to that, he would add the first thing, which is x squared plus five x, times the derivative of the second thing. So the derivative of sine of x is cosine of x. So this is what we should have been seeing at this step right over here. He shouldn't have just taken the product of the derivatives, he should have applied the product rule. So his work is not correct, and his mistake is that he didn't apply the product rule. He just assumed that the derivative of the products is the same thing as the product of the derivatives. Let's do more examples.