Question

F(x) = (5x^3 + 4)^3 find second deravitive F’(x) = 3(5x^3 + 4)3-1 (15x^2) = (45x2) (5x^3 + 4)2 F”(X) = (45x^2) (5x^3 + 4)2

(45x^2)*2(5x^3 + 4)*15x2] + [90x * 90(5x^3 + 4)^2]

how to open this up

Answer 1

my eyes are burning!!

Answer 2

F(x) = (5x^3 + 4)^3

F'' = 3(5x^3 + 4)^2 . 15x^2

Answer 3

\(F(x)=(5x^3+4)^3\)
\(F'(x)=3(5x^3+4)^2\cdot 15x^2\)
\(F''(x)=90x\cdot (5x^3+4)^2+90x^2(5x^3+4)\cdot 15x^2\)

Answer 4

that was sposed to be F'....

F'' = 3(5x^3 + 4)^2 . 30x + 6(5x^3 + 4) 15x^2 15x^2

Answer 5

right now what after that step

Answer 6

that is the second derivative

Answer 7

how do you open that up

Answer 8

you only derive twice to find the second derivative....

Answer 9

understood how do you open teacher wants us to open

Answer 10

if you wanna expand it; then multiply it out..... right?

Answer 11

90x(25x^6 + 16 + 20x^3) + 15.15.6.x^4(5x^3 +4)

Answer 12

90x(25x^6 + 16 + 20x^3) + 1350x^4(5x^3 +4)

90(25)x^7 + (90x)16 + (90)20x^4 + 1350(5)x^7 +4(1350x^4) if i did it right

Answer 13

your first derivative is wrong it should be 3(5x^3 + 4)3-1 (15x^2) = (45x2) (5x^3 + 4)^2

Answer 14

3(5x^3 + 4)^2 (15x^2) = (45x^2) (5x^3 + 4)^2

Answer 15

F' = 3(5x^3 + 4)^2 . 15x^2 this? not according to what you gave us...

Answer 16

(5x^3 + 4)^3

Answer 17

original right

Answer 18

derivative of inner

Answer 19

* chain rule

Answer 20

F' = 45x^2 (5x-4)^2 ... we agree :)

Answer 21

k lol

Answer 22

now 2nd derivative

Answer 23

to make things easier; we could just expand this right here and take the derivative afterwards

Answer 24

smart

Answer 25

so

Answer 26

i have my moments lol

Answer 27

so 25x - 40x + 16

Answer 28

45x^2(25x^6 -40x^3 +16) right?

Answer 29

* 45x^2

Answer 30

how to the 6th

Answer 31

1125x^8 -1800x^5 + 720x^2

Answer 32

5.5.x^3.x^3 = 25x^6

Answer 33

http://www.wolframalpha.com/input/?i=d^2%2Fdx^2%28%285x^3+%2B+4%29^3%29

Answer 34

its to the ^2

Answer 35

-4.-4 = +16

5.-4.2.x^3 = -40x^3

Answer 36

just the innards; exapnding the ^2 part....

Answer 37

then multiply in the 45x^2 after that

Answer 38

oh you did product + chain rule

Answer 39

1125x^8 -1800x^5 + 720x^2 is what you should get

Answer 40

check this link http://www.wolframalpha.com/input/?i=d^2%2Fdx^2%28%285x^3+%2B+4%29^3%29 it says diff

Answer 41

45x^2 (5x^3 -4)^2

45x^2(25x^6 -40x^3 +16)

1125x^8 -1800x^5 + 720x^2

all i did was expand it to get to here; no second derivative yet..

Answer 42

ahhh

Answer 43

now we can easily...or easilier... take the deriavtive of this

Answer 44

yup

Answer 45

1125(8)x^7 -1800(5)x^4 + 720(2)x

9000x^7 -9000x^4 + 1440x if i kept track of it all

Answer 46

factor out the 360x now

Answer 47

and it should match wolframs

Answer 48

360x (25x^6 -25x^3 +4)

Answer 49

only diff is that I got a negative from a typo in the beginning

Answer 50

thanks man

Answer 51

youre welcome :)