Derivatives

[KidInkFan]

Hi,

need help for following question:

C = 6(2sqrt(I^3)+5)/(I+10)

I thought I would expand the 6 out and apply the quotient rule, but im still not getting it right... I just dont understand what I'm doing wrong....

when i expand and take the derivative of the function i get:

(12(I^(3/2))+30)'(I+30)-(I+30)'(12(I^(3/2))+30)'/(I+30)^2

Am i doing this right??

 

[Bob Brown MSEE]

I get

Let x=I so its easier to read
(180x^(1/2)+6x^(3/2)-30) / (x^2+20x+100)

 

[HallsofIvy]

Hopefully, even easier to read:
\(\displaystyle \frac{6(2I^{3/2}+ 5)}{I+ 10}= \frac{12I^{3/2}+ 30}{I+ 10}\)

You then have
(12(I^(3/2))+30)'(I+30)-(I+30)'(12(I^(3/2))+30)'/(I+30)
Your basic idea is correct. But the first term is the derivative of \(\displaystyle 12I^{3/2}+ 30\) times I+ 10, NOT "I+ 30" as you have. I suspect that was a typo. Then you the derivative of (I+ 30) times \(\displaystyle 12I^{3/2}+ 30\). You do NOT want the derivative of \(\displaystyle 12I^{3/2}+ 30\) in the second term. I suspect that was also a typo. Go ahead and do those derivatives and simplify. But be careful to proof read in the future! (Believe me, I have lots of experience with typos messing things up!)

 

[lookagain]

Let x=I so its easier to read

(180x^(1/2) + 6x^(3/2) - 30)/(x^2 + 20x + 100)

Now, it is significantly easier to read.

1) Spread out terms more.

2) Don't have any spaces between the close parenthesis and the "/", as well as between the "/"
and the open parenthesis.

3) Also, as was demonstrated with the post to which was amended, the "^" was used
for exponentiation. Therefore, for instance, in typing terms of polynomials, it is
expected and consistent to no longer type "xx" for "x^2," "xxx" for "x^3," and so on,
henceforth.

 

[lilvinc]

(x 1)/x

 

[JeffM]

(x 1)/x

And what pray tell is your question?