Question

f(x)=(3x^4)*sqrt(x) + 7/x^2*(sqrt(x))
f '(x)= ??

Answer 1

change the square root to an exponent

Answer 2

3x^4 x^(1/2) + 7/(x^2 x^(1/2))

Answer 3

3x^(9/2) + 7/(x^5/2) and work that....

Answer 4

do you know how to do a derivative?

Answer 5

7/(x^5/2) is its own term right? or is that (x^(5/2)) the demoniator of the whole equation?

Answer 6

d..e...n..o..m...i..n...a..t...o....r.. lol

Answer 7

own term

Answer 8

haha

Answer 9

good... :)

Answer 10

o shoot , i thought i was replying to you but it wasnt posting

Answer 11

yes, i know how to find derivatives

Answer 12

i just dont know where i am going wrong

Answer 13

step me thru what you have done and I will let you know :)

Answer 14

(i had made them exponents as well)

Answer 15

the first term is a breeze.... just multiply exponent and subtract "1" from it.....

Answer 16

3x^(9/2) = 3(9/2)x^(7/2) =

27 x^(7/2)
---------
2

right?

Answer 17

sorry got kicked out, yes that is what i have

Answer 18

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

Answer 19

7
-------- how would you derive this term?
(x^(5/2))

Answer 20

ok

Answer 21

oo i had x^3/2 not x^5/2

Answer 22

quotient rule:

I remember it like this:

BT'-B'T
------ where B=bottom, and T=top
B^2

Answer 23

whose right then, me or you :)

Answer 24

when you are combining x^2 and x^1/2 dont you add the exponents?

Answer 25

yes... 2 + 1/2 = a mixed numeral...tern it into an improper fraction

2(2)+1 5
------ = ---
2 2

Answer 26

lol...a tern is a sea bird i think

Answer 27

7
-------- lets derive this...
(x^(5/2))

Answer 28

oo duh.

Answer 29

ok simple addition.

Answer 30

so that would be--

Answer 31

-35/2x^7/2

Answer 32

may i ask you one more derivative question?

Answer 33

5 x^(3/2)
B' = -------- and T' = 0
2

-35 x^(3/2)
--------------
2
------------------
x^5

Is what I get...

Answer 34

sure, but lets finish this one first :)

Answer 35

i plugged it in my school system and got the right answer :)

Answer 36

lol ... cheater :)

Answer 37

next question?

Answer 38

they dont tell you what the answer is, just if you get it correct ;)

Answer 39

if f(x) = sqrt(6x)
f 'x = ?

Answer 40

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?

Answer 41

change to exponent

Answer 42

ok....

sqrt(6x) = (6x)^(1/2) ....might have to still do the "extra" because of that (6x) in there...

Answer 43

ok

Answer 44

is this correct-- 1/(2(6x)^1/2)

Answer 45

(1/2)(6x)^(-1/2) cleans up to:

1
-------- ;we got to multiply (use the chain rule) to use that "6x"
2sqrt(6x)

Answer 46

that didnt turn out the way I wanted lol

Answer 47

1
------- times Dx(6x)
2sqrt(6x)

Answer 48

Dx(6x) = 6

Answer 49

i dont understand why you are taking the derivative of 6x

Answer 50

6/2 = 3

3
-------
sqrt(6x)

Answer 51

let me explain it like this:

remember when we have f(g(x)) and want to derive it?

Answer 52

we have to use the "chain rule" to solve it right?

this problem is exactly that set up, let me show you..

Answer 53

sorry, keep getting kicked out. i havent learned the chain rule

Answer 54

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?

Answer 55

yes

Answer 56

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?

Answer 57

ah, yes

Answer 58

now i understand how you got to your final answer. thank you so much for all of your help!!!

Answer 59

youre welcome :)

Answer 60

definitely a 'fan' of you :)

Answer 61

:) thanx...