1. ## Derivative Question Problems

Can someone please give me the full detailed solutions for both problems? The questions are to find the derivative functions of these functions (using the quotient rule).

Problem 1:

y = (r^2)/(1 + sqrt(r))

Problem 2:

f(x) = x/(c + c/x)

Answer (1): y' = r(4 + 3sqrt(r))/2(1 + sqrt(r))^2
Answer (2): y' = 2cx/(x^2 + c)^2

Any help would be greatly appreciated!

2. Originally Posted by s3a
Can someone please give me the full detailed solutions for both problems? The questions are to find the derivative functions of these functions (using the quotient rule).

Problem 1:

y = (r^2)/(1 + sqrt(r))

Problem 2:

f(x) = x/(c + c/x)

Answer (1): y' = r(4 + 3sqrt(r))/2(1 + sqrt(r))^2
Answer (2): y' = 2cx/(x^2 + c)^2

Any help would be greatly appreciated!
$y = \frac{r^2}{1+\sqrt{r}}$

$y' = \frac{(1+\sqrt{r})(2r) - (r^2)\left(\frac{1}{2\sqrt{r}}\right)}{(1+\sqrt{r} )^2}$

you clean up the algebra

for the second one, start by multiplying numerator and denominator by x to clear the fraction in the denominator ...

$f(x) = \frac{x^2}{cx + c}$

now use the quotient rule.

3. I got those steps right so that's not my problem. By the way, you didn't add the primes on y' = derivative_function.

4. Originally Posted by s3a
I got those steps right so that's not my problem. [snip]
Then how about you show all your workoing so that we can see what is your problem. Or just use this website: http://www.wolframalpha.com/.
Originally Posted by s3a
[snip]By the way, you didn't add the primes on y' = derivative_function.
Tsk tsk skeeter. Your pay will be docked this week. (Sheesh, that's the thanks you get ....).

5. Originally Posted by s3a
I got those steps right so that's not my problem. By the way, you didn't add the primes on y' = derivative_function.
huh?

6. Originally Posted by s3a
I got those steps right so that's not my problem. By the way, you didn't add the primes on y' = derivative_function.
There is no indication that he went back and editted after you wrote this and I certainly see a ' on his derivative!

7. I guess I came off as rude, I obviously didn't mean that. But with the y' = derivative_function, I meant the stuff after the y' = has 2 " ' " signs missing. My work is attached as a pdf file. (#17, #25)

8. Originally Posted by s3a
I guess I came off as rude, I obviously didn't mean that. But with the y' = derivative_function, I meant the stuff after the y' = has 2 " ' " signs missing. My work is attached as a pdf file. (#17, #25)
did it ever occur to you that those 'prime' signs are not necessary?

note that $2r = (r^2)'$

9. Oh yes you're right, I skimmed through it but my teacher basically explained both to me in person so I get them but thanks for the effort and sorry if I offended you or something.