This video from IntegralCALC shows you how to solve the Quotient Rule f(x)=(2x^3-3x^2+4x-5)/(x^2) Math problem.
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Quotient Rule f(x)=(2x3-3x2+4x-5)/(x2) Hi everyone. We’re going to do another quotient rule problem. I went ahead and left the formula from the previous problems and I’m just going to go ahead and write the problem that we’re doing right now, which is f(x)=(2x3-3x2+4x-5)/(x2). So, the top here, 2x3-3x2+4x-5 is our f(x) and g(x) is x2 in our problem. So now we just need to go through and apply this formula to this problem in order to take the derivative of this function. So, the derivative, f1(x) is going to look like this. The derivative of the top, f(x), we need the derivative of the top here. So that’s going to be 6x2-6x+4 times the bottom without doing anything to it, x2 minus the top without doing anything to it so 2x3-3x2+4x-5 times the derivative of g(x) which is the bottom, which is x2. So times 2x, and then we’ve got everything on the top so now we need to do is square the denominator. So g(x) is the bottom so x2. So we say, x2, but then of course we square it. So, add a squared there. And if you don’t mind, I will go ahead and erase this so that we can go through and simplify this together. I'm going to go ahead and multiply out the x2 and the 2x so that we can simplify this and try to cancel some terms. So, we will say 6x4-6x3+4x2 and we’ve now distributed the x2. Now, we need to distribute the 2x so we will say -4x4, and this is going to be -6x3, but because we’ve got a minus there, it’s going to be +6x3, and then +48x so -8x2, and then -10x. So, that’s the top. Let’s go ahead and simplify that before we go forward. We have 6x4-4x4 which is going to be 2x4, and then we have -6x3+6x3 which means those cancel and go away. 4x2-8x2 means we’re looking at -4x2, and then -10x is the top. So now, what I would like to do is go ahead and factor out again. Actually you know what before we do that, let’s go ahead and say we’ve left out the denominator this whole time so we’re going to go ahead and simplify this to be x4. So now what we can do is we can cancel out an x because we have one here. So, this is going to be x3, we’re going to cancel out one x from every term. And that’s the most that we can do because we only have one x here. So, this one is going to go away from this here. The denominator becomes x3 and this becomes simply x instead of x2 and this is going to become x3 here. And the only thing I would say to do is factor out a two from the top. So, we’ll go ahead and say 2*x3-2x-5/x3, and that is your answer using the quotient rule on this function here. Thanks guys.
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