anonymous
  • anonymous
how to find the derivative of [(x+5)/(x^2+2)]^2
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
uhm.. what?
mathmale
  • mathmale
First off, you've done a nice job of presenting this function: [(x+5)/(x^2+2)]^2.\[ [(x+5)/(x^2+2)]^2. What kind of function is this? I see several different types of functions here: a power, a quotient, a square, a sum, etc.
mathmale
  • mathmale
These functions are nested within one another. What's the outermost function?

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anonymous
  • anonymous
uhm im not sure..
anonymous
  • anonymous
i know we have to use the chain rule and the quotient rule, I just need help with the steps
mathmale
  • mathmale
The outermost function is the squaring function. You see [ ]^2.
mathmale
  • mathmale
what type of function do you see within those brackets?
anonymous
  • anonymous
uhm a quotient
mathmale
  • mathmale
Right. And the quotient has another type of function in the numerator and another type in the denominator. What would be the very first step towards finding the derivative of this complicated function? I'd prefer you label your function with "y = ".
anonymous
  • anonymous
uhm i think we would bring the 2 to the front..is that right? and okay got it
mathmale
  • mathmale
Right. What's next? Hint: What's inside the [ ]?
anonymous
  • anonymous
okay so it'll look like this 2[x^2+2](1)
mathmale
  • mathmale
Hope I didn't tell you that that was correct. What is correct, so far, is that you now have\[\frac{ dy }{ dx }=2[ ] \]
mathmale
  • mathmale
with a quotient inside the brackets [ }. I'd suggest you write out the whole thing to ensure that we don't lose anything.
mathmale
  • mathmale
The fraction about which we're talking is (x+5)/(x^2+2). Your next step is to apply the quotient rule to find the derivative of this quotient.
anonymous
  • anonymous
well, actually the whole thing is squared.
anonymous
  • anonymous
or okay never mind.. we already moved the two to the front right?
mathmale
  • mathmale
True, to start with. That was the function y. But now we're finding the derivative, y ', and the form of that will be dy/dx = 2{ }^1, with that quotient inside. find the derivative of the quotient now. You might want to review the quotient rule first.
anonymous
  • anonymous
so uh we'll have 2(x^2+2)(1)-(x+5)(2x)/(x^2+2)^2

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