anonymous
  • anonymous
f(x)=(3x^4)*sqrt(x) + 7/x^2*(sqrt(x)) f '(x)= ??
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
amistre64
  • amistre64
change the square root to an exponent
amistre64
  • amistre64
3x^4 x^(1/2) + 7/(x^2 x^(1/2))
amistre64
  • amistre64
3x^(9/2) + 7/(x^5/2) and work that....

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

amistre64
  • amistre64
do you know how to do a derivative?
amistre64
  • amistre64
7/(x^5/2) is its own term right? or is that (x^(5/2)) the demoniator of the whole equation?
amistre64
  • amistre64
d..e...n..o..m...i..n...a..t...o....r.. lol
anonymous
  • anonymous
own term
anonymous
  • anonymous
haha
amistre64
  • amistre64
good... :)
anonymous
  • anonymous
o shoot , i thought i was replying to you but it wasnt posting
anonymous
  • anonymous
yes, i know how to find derivatives
anonymous
  • anonymous
i just dont know where i am going wrong
amistre64
  • amistre64
step me thru what you have done and I will let you know :)
anonymous
  • anonymous
(i had made them exponents as well)
amistre64
  • amistre64
the first term is a breeze.... just multiply exponent and subtract "1" from it.....
amistre64
  • amistre64
3x^(9/2) = 3(9/2)x^(7/2) = 27 x^(7/2) --------- 2 right?
anonymous
  • anonymous
sorry got kicked out, yes that is what i have
amistre64
  • amistre64
x^(7/2) = x^(6/2) x^(1/2) so if you want to clean it up some: 17 x^3 sqrt(x) ------------ for the first term... 2
amistre64
  • amistre64
7 -------- how would you derive this term? (x^(5/2))
anonymous
  • anonymous
ok
anonymous
  • anonymous
oo i had x^3/2 not x^5/2
amistre64
  • amistre64
quotient rule: I remember it like this: BT'-B'T ------ where B=bottom, and T=top B^2
amistre64
  • amistre64
whose right then, me or you :)
anonymous
  • anonymous
when you are combining x^2 and x^1/2 dont you add the exponents?
amistre64
  • amistre64
yes... 2 + 1/2 = a mixed numeral...tern it into an improper fraction 2(2)+1 5 ------ = --- 2 2
amistre64
  • amistre64
lol...a tern is a sea bird i think
amistre64
  • amistre64
7 -------- lets derive this... (x^(5/2))
anonymous
  • anonymous
oo duh.
anonymous
  • anonymous
ok simple addition.
anonymous
  • anonymous
so that would be--
anonymous
  • anonymous
-35/2x^7/2
anonymous
  • anonymous
may i ask you one more derivative question?
amistre64
  • amistre64
5 x^(3/2) B' = -------- and T' = 0 2 -35 x^(3/2) -------------- 2 ------------------ x^5 Is what I get...
amistre64
  • amistre64
sure, but lets finish this one first :)
anonymous
  • anonymous
i plugged it in my school system and got the right answer :)
amistre64
  • amistre64
lol ... cheater :)
amistre64
  • amistre64
next question?
anonymous
  • anonymous
they dont tell you what the answer is, just if you get it correct ;)
anonymous
  • anonymous
if f(x) = sqrt(6x) f 'x = ?
amistre64
  • amistre64
2 ways to do this; we can do a substituion and the chain rule? or simply change to exponent and solve it.. which way you want it?
anonymous
  • anonymous
change to exponent
amistre64
  • amistre64
ok.... sqrt(6x) = (6x)^(1/2) ....might have to still do the "extra" because of that (6x) in there...
anonymous
  • anonymous
ok
anonymous
  • anonymous
is this correct-- 1/(2(6x)^1/2)
amistre64
  • amistre64
(1/2)(6x)^(-1/2) cleans up to: 1 -------- ;we got to multiply (use the chain rule) to use that "6x" 2sqrt(6x)
amistre64
  • amistre64
that didnt turn out the way I wanted lol
amistre64
  • amistre64
1 ------- times Dx(6x) 2sqrt(6x)
amistre64
  • amistre64
Dx(6x) = 6
anonymous
  • anonymous
i dont understand why you are taking the derivative of 6x
amistre64
  • amistre64
6/2 = 3 3 ------- sqrt(6x)
amistre64
  • amistre64
let me explain it like this: remember when we have f(g(x)) and want to derive it?
amistre64
  • amistre64
we have to use the "chain rule" to solve it right? this problem is exactly that set up, let me show you..
anonymous
  • anonymous
sorry, keep getting kicked out. i havent learned the chain rule
amistre64
  • amistre64
y = sqrt(u) and u = 6x to solve dy/dx we need the chain rule: (dy/dx) = (dy/du) (du/dx) y = sqrt(u) dy/du = 1/2sqrt(u) u = 6x du/dx = 6 Do you see it?
anonymous
  • anonymous
yes
amistre64
  • amistre64
Do you understand it? Imagine a set of gears that are meshed together, when the first one is turned, all the others turn as well. But they depend on the funtion of the first one to determine how they are going to behave.... does that makes sense?
anonymous
  • anonymous
ah, yes
anonymous
  • anonymous
now i understand how you got to your final answer. thank you so much for all of your help!!!
amistre64
  • amistre64
youre welcome :)
anonymous
  • anonymous
definitely a 'fan' of you :)
amistre64
  • amistre64
:) thanx...

Looking for something else?

Not the answer you are looking for? Search for more explanations.