Question

how to find the derivative of [(x+5)/(x^2+2)]^2

Answer 1

uhm.. what?

Answer 2

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.

Answer 3

These functions are nested within one another. What's the outermost function?

Answer 4

uhm im not sure..

Answer 5

i know we have to use the chain rule and the quotient rule, I just need help with the steps

Answer 6

The outermost function is the squaring function. You see [ ]^2.

Answer 7

what type of function do you see within those brackets?

Answer 8

uhm a quotient

Answer 9

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 = ".

Answer 10

uhm i think we would bring the 2 to the front..is that right? and okay got it

Answer 11

Right. What's next? Hint: What's inside the [ ]?

Answer 12

okay so it'll look like this 2[x^2+2](1)

Answer 13

Hope I didn't tell you that that was correct. What is correct, so far, is that you now have\[\frac{ dy }{ dx }=2[ ] \]

Answer 14

with a quotient inside the brackets [ }. I'd suggest you write out the whole thing to ensure that we don't lose anything.

Answer 15

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.

Answer 16

well, actually the whole thing is squared.

Answer 17

or okay never mind.. we already moved the two to the front right?

Answer 18

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.

Answer 19

so uh we'll have 2(x^2+2)(1)-(x+5)(2x)/(x^2+2)^2