anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
my eyes are burning!!
amistre64
  • amistre64
F(x) = (5x^3 + 4)^3 F'' = 3(5x^3 + 4)^2 . 15x^2
watchmath
  • watchmath
\(F(x)=(5x^3+4)^3\) \(F'(x)=3(5x^3+4)^2\cdot 15x^2\) \(F''(x)=90x\cdot (5x^3+4)^2+90x^2(5x^3+4)\cdot 15x^2\)

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amistre64
  • amistre64
that was sposed to be F'.... F'' = 3(5x^3 + 4)^2 . 30x + 6(5x^3 + 4) 15x^2 15x^2
anonymous
  • anonymous
right now what after that step
amistre64
  • amistre64
that is the second derivative
anonymous
  • anonymous
how do you open that up
amistre64
  • amistre64
you only derive twice to find the second derivative....
anonymous
  • anonymous
understood how do you open teacher wants us to open
amistre64
  • amistre64
if you wanna expand it; then multiply it out..... right?
amistre64
  • amistre64
90x(25x^6 + 16 + 20x^3) + 15.15.6.x^4(5x^3 +4)
amistre64
  • amistre64
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
anonymous
  • anonymous
your first derivative is wrong it should be 3(5x^3 + 4)3-1 (15x^2) = (45x2) (5x^3 + 4)^2
anonymous
  • anonymous
3(5x^3 + 4)^2 (15x^2) = (45x^2) (5x^3 + 4)^2
amistre64
  • amistre64
F' = 3(5x^3 + 4)^2 . 15x^2 this? not according to what you gave us...
anonymous
  • anonymous
(5x^3 + 4)^3
anonymous
  • anonymous
original right
anonymous
  • anonymous
derivative of inner
anonymous
  • anonymous
* chain rule
amistre64
  • amistre64
F' = 45x^2 (5x-4)^2 ... we agree :)
anonymous
  • anonymous
k lol
anonymous
  • anonymous
now 2nd derivative
amistre64
  • amistre64
to make things easier; we could just expand this right here and take the derivative afterwards
anonymous
  • anonymous
smart
anonymous
  • anonymous
so
amistre64
  • amistre64
i have my moments lol
anonymous
  • anonymous
so 25x - 40x + 16
amistre64
  • amistre64
45x^2(25x^6 -40x^3 +16) right?
anonymous
  • anonymous
* 45x^2
anonymous
  • anonymous
how to the 6th
amistre64
  • amistre64
1125x^8 -1800x^5 + 720x^2
amistre64
  • amistre64
5.5.x^3.x^3 = 25x^6
anonymous
  • anonymous
http://www.wolframalpha.com/input/?i=d^2%2Fdx^2%28%285x^3+%2B+4%29^3%29
anonymous
  • anonymous
its to the ^2
amistre64
  • amistre64
-4.-4 = +16 5.-4.2.x^3 = -40x^3
amistre64
  • amistre64
just the innards; exapnding the ^2 part....
amistre64
  • amistre64
then multiply in the 45x^2 after that
anonymous
  • anonymous
oh you did product + chain rule
amistre64
  • amistre64
1125x^8 -1800x^5 + 720x^2 is what you should get
anonymous
  • anonymous
check this link http://www.wolframalpha.com/input/?i=d^2%2Fdx^2%28%285x^3+%2B+4%29^3%29 it says diff
amistre64
  • amistre64
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..
anonymous
  • anonymous
ahhh
amistre64
  • amistre64
now we can easily...or easilier... take the deriavtive of this
anonymous
  • anonymous
yup
amistre64
  • amistre64
1125(8)x^7 -1800(5)x^4 + 720(2)x 9000x^7 -9000x^4 + 1440x if i kept track of it all
amistre64
  • amistre64
factor out the 360x now
amistre64
  • amistre64
and it should match wolframs
amistre64
  • amistre64
360x (25x^6 -25x^3 +4)
amistre64
  • amistre64
only diff is that I got a negative from a typo in the beginning
anonymous
  • anonymous
thanks man
amistre64
  • amistre64
youre welcome :)

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