Question

can somebody check my work with this derivative problem?

Answer 1

(x^2-1)^5/2 (x^3+1)

Answer 2

i'll post my work

Answer 3

ok, show to me.. what did u get

Answer 4

first heres my derivatives: f(x)=(x^2-1)^5/2 f'=5x(x^2-1)^3/2

Answer 5

g(x) = x^3+1 g'= 3x^2

Answer 6

good so far?

Answer 7

for the first, f(x) = (x^2-1)^5/2 or (x^2-1)^(5/2) ?

Answer 8

(x^2-1)^(5/2)

Answer 9

f' = 5/2*(x^2-1)^(3/2)*2x = 5x(x^2-1)^(3/2)
u are right

Answer 10

ok

Answer 11

so now i will show how i use the product rule

Answer 12

yeps..

Answer 13

(x^2-1)^(5/2) (3x^2)+ (5x(x^2-1)^(3/2) (x^3+1)

Answer 14

yea, same what i got....

Answer 15

ok cool

Answer 16

yep... any else

Answer 17

yea i had trouble multiplying everything out, here is what i got

Answer 18

(3x^4-3x^2)^(5/2) + (15x^6+5x^3-15x^4-5x)^(3/2)

Answer 19

is it the expand ur answer before ?

Answer 20

i dont understand your question

Answer 21

ohh... maybe this ur new question

Answer 22

no, this is what i got when i multiplied everything out, i just dont know if i did it correctly

Answer 23

ohhhhh.... sorry, misscomunication :)

Answer 24

no worries :D

Answer 25

from ur anwer above (x^2-1)^(5/2) (3x^2)+ (5x(x^2-1)^(3/2) (x^3+1)
we cant do multiplying 3x^2 with (x^2-1)^(5/2), becasue the power each terms not same

Answer 26

oh ok

Answer 27

so what do we do?

Answer 28

im scared

Answer 29

i think, at the first is well..... but if u want simplify again, maybe it can be
(x^2-1)^(3/2)*{5x(x^3+1) + 3x(x^2-1)} =
(x^2-1)^(3/2)*{5x^4+5x) + 3x^3-3x} = it just manipulating algebra

Answer 30

i think you made a mistake on this part

Answer 31

{5x(x^3+1) + 3x(x^2-1)} = (x^2-1)^(3/2)*{5x^4+5x) + 3x^3-3x} = it just manipulating algebra

Answer 32

i have factored out
which part ? :)

Answer 33

idk where you got the 5x^4 from. the equation was 5x(x^2-1)^(3/2)

Answer 34

5x*(x^3 + 1) = 5x^4 + 5x, right ?

Answer 35

(x^2-1)^(5/2) (3x^2)+ (5x(x^2-1)^(3/2) (x^3+1)

Answer 36

hint : x^m * x^n = x^(m+n)

Answer 37

oh you took the 5x and multiplied it with the (x^3+1)

Answer 38

yes....
from ur answer we can take common factor out to factor it

Answer 39

hmmmmmmmmmmm

Answer 40

the common factor of them is (x^2-1)^(3/2), right ?

Answer 41

but only one of them is ^(3/2)

Answer 42

there is one (x^2-1)^(5/2) and the other is (x^2-1)^(3/2)

Answer 43

so i dont think the common factor is true

Answer 44

well, i will give u a simple problem... what is the common factor of x^(3/2) and x^(5/2) ?

Answer 45

x?

Answer 46

wrong.. :)

Answer 47

x(^3/2)

Answer 48

ooooo

Answer 49

opss.. x^(3/2) i meant

Answer 50

so what happens to the (x^2-1)^(5/2) it just becomes (x^2-1)^(3/2)?

Answer 51

(x^2-1)^(5/2) = (x^2-1)^(3/2) * (x^2-1)
look the powers (3/2 + 1 = 5/2, right)

Answer 52

oh true! ahhaha i see now

Answer 53

ok. is it cleared

Answer 54

ok so we have: (x^2-1)^(3/2)*{5x^4+5x) + 3x^3-3x}

Answer 55

yeah...

Answer 56

we can work some stuff out in there

Answer 57

(x^2-1)^(3/2) *(5x^4+3x^3+2x)

Answer 58

u are right, 5x-3x = 2x, i didnt simplify it

Answer 59

yay!

Answer 60

so now we multiply these two out? darn :(

Answer 61

no... that is the finally answer, we cant multiply of them again:)

Answer 62

i mean, the power of (x^2-1) not same with (5x^4+3x^3+2x). so, can not be multiplied

Answer 63

oh ok cool! thanks so much for your help!

Answer 64

very welcome