This video from IntegralCALC shows you how to solve the Quotient Rule f(x)=3/(x^2+x+1) Math problem.
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Quotient Rule f(x) = 3/(x2+x+1) Hey guys, another quotient rule problem. I actually just left this out from the last problem so that we could reference it. It is the formula for the quotient rule formula, and it’s a formula that helps you take the derivative of different kinds of functions. So the problem that we’re going to be doing is f(x) = 3/(x2 + x + 1). So three is our f(x) and x2 + x + 1 is g(x), and we’re just going to apply this formula to this function to take the derivative. So, let’s go ahead and take the derivative. We’ll call it at kind of x and we’ll just follow this term-by-term. So the first thing we got to do is find f1(x) because that’s this first one here. So f1(x). So f(x) is the top, which means we need to take the derivative of the top, which means we need to take the derivative of three. The derivative of three, because there is a constant is just zero. So we’ll go ahead and write that. And then we would multiply it by g(x), which is the bottom. So we multiply it by x2+ x + 1. But since we’ve got zero here, we know that’s going to cancel so we don’t need to write out x2+ x + 1 for g(x). So we’re just going to leave that alone. So that mostly a minus and f(x), it’s the top which is three. So we can say three times the derivative of the bottom, g(x) here, so the derivative of x2+ x + 1. So we’ll multiply it and we’ll say the derivative of the bottom here is 2x, the derivative of x2+ 1, the derivative of x, and the one goes away because the derivative of a constant is always zero. So, that is now the top of our new derivative function. So we go ahead and do the denominator which is just g(x)2, we have g(x) here, it’s the bottom. So we need to do the bottom squared. So we have x2 + x + 1, which is the bottom but then of course we’ve got to square it, so we add a squared. And the only thing that I would do to simplify this is personally, it’s just person’s preference, I would multiply this and just get rid of the zero. So I’m going to write my final answer as -6x- 3/x2 + x + 12. You could leave it as -3 × 2x + 1 over the bottom, either way is fine but either way, this is the answer.

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