 In this video, we provide the solution to question number six for practice exam number three for math 12 10 And we're asked to compute the derivative of the function f of x equals e to the x over x squared plus two This because our function is a fraction. We're going to use the quotient rule to calculate its derivatives So remember our poem here. We're going to get low D high take the derivative e to the x minus high d low Square the bottom here we go some things to remember about the quotient rule is don't try to do too much at once use some scratch paper Or use the margins in the page to write it out if you need to Also, don't actually multiply out the denominator leave it factored. That should be a square not a prime there And so now let's try to simplify these remaining derivatives here. We get x squared plus 2x derivative e to the x It's itself e to the x then we get a minus e to the x we take the derivative x squared plus 2x That gives us a 2x plus 2 and this all sits above the x squared plus 2x Squared now when you look at the answers none of those quite look like what we want. I It turns out we need to simplify things a little bit So let's factor out the e to the x and then see what polynomials left behind x squared plus 2x We get a minus 2x minus 2 remember this negative sign will distribute on to both of these pieces And this sits above the denominator x squared plus 2x quantity squared Notice now once you've explained once you factor out the e to the x the 2x is cancel out You're left with x squared minus 2 you have an e to the x you have this is all above x squared plus 2x squared x squared over 2x squared that's right So we see that the correct answer would be a using the quotient rule