1. ## Another derivative question

Sorry, I just couldn't find out by my self

Anyone got a clue for these three question?

f(x) = (x^2 - 24) / (x+2)

y= ln(x tan x)

I know it looks very simple but I'm totally lost.

Please give me a hint for those two ,

Thank you.

2. For these sorts of problems, you have to kind of "reverse the order" of evaluation. Take f(x) = (x^2 - 24) / (x+2). The last arithmetic operation you would do in evaluating the function at a point would be the division. Therefore, that's the first thing you differentiate. What is the quotient rule?

For the second function, you work from outside in. You'll need the chain rule as well as the product rule. What do you get?

3. For the 1st question, I used quotient rule and got
x^2+4x+24/(x+2)^2
Hope it's right, thanks.

For the 2nd question,
Would it be same as (ln x)(ln tan x)???
I have no idea how to start this.

4. Your answer to the first question is correct, but ONLY if you put in parentheses like so:

$x^2+4x+\dfrac{24}{(x+2)^{2}},$ whereas the correct answer is this:

$\dfrac{x^{2}+4x+24}{(x+2)^{2}}.$ They are not the same!

For the second problem, I don't think you understand yet. What is the chain rule? How does it apply here? What is the outermost function?

5. Ok, thanks for the help.
To start off, would it be..
let's say u = ln(v) and v = (x tan x)
1/(x tan x) (1 sec^2 x) ?

6. Closer. However, you have not taken the derivative of the argument of the logarithm function correctly. What's going on inside the logarithm?

7. In the logarithm, I can only think of the first x becoming to be 1 after the derivative, and tan x becoming sec^2 x..
Would there be any other method to solve (x tan x)?

8. Oh, I used product rule on (x tan x).
As a result I got
(tan x + x sec^2 x)
Therefore, to substitute this into the chain rule,
1/(x tan x) (tan x + x sec^2 x)
Is this right?
Btw, thank you verrry much for the help again

9. Yeah, that's looking better. I would probably write the answer as

$\dfrac{\tan(x) + x \sec^{2}(x)}{x\tan(x)}.$

Then it's perfectly clear what is in the argument of each trig function, and what's in the numerator and denominator of the fraction.

10. Thanks alot Ackbeet.
I really get it now
You are my master!
Thank you!

11. You're welcome for the help, but please don't make me your master.