anonymous
  • anonymous
F(x) = (5x3 + 4)3 find the second derivative
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
step by step please
anonymous
  • anonymous
I assume that the 3 is a power?
anonymous
  • anonymous
well i used chain rule

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More answers

anonymous
  • anonymous
f'(x)=3(5x3 + 4)^2[15x^2]
anonymous
  • anonymous
[45(x2)](2)(5x3 +4)1(15x3-1) + (45x2) (5x3 + 4)2
anonymous
  • anonymous
\[45(5x^3+4)(x^2)\]
anonymous
  • anonymous
oh again missed the exponent 2
anonymous
  • anonymous
is my first step corrrect
anonymous
  • anonymous
\[f'(x)=45(5x^3+4)^2(x^2)\]
anonymous
  • anonymous
(45x2) (5x3 + 4)2
anonymous
  • anonymous
3 is not in power?
anonymous
  • anonymous
right, now how to do second derivative
anonymous
  • anonymous
use product rule
anonymous
  • anonymous
F(x) = (5x^3 + 4)^2
anonymous
  • anonymous
is the questions
anonymous
  • anonymous
wait your derivative doesnt seem right
anonymous
  • anonymous
this is not the same u posted earlier
anonymous
  • anonymous
oh no its to the third power
anonymous
  • anonymous
but the way you wrote the answer is different
anonymous
  • anonymous
(45x^2) (5x3 + 4)2 by using chain rule
anonymous
  • anonymous
then the derivative is correct:)
anonymous
  • anonymous
right
anonymous
  • anonymous
now use the product rule
anonymous
  • anonymous
you left the 45 and x^2 separately
anonymous
  • anonymous
confused me
anonymous
  • anonymous
y confused?
anonymous
  • anonymous
45(5x3+4)(x2)
anonymous
  • anonymous
how can you separate 45 from the equation
anonymous
  • anonymous
this is the second step, read the first too
anonymous
  • anonymous
y seperated? it is being multiplied
anonymous
  • anonymous
ok let me me work it out and see if our answers match
anonymous
  • anonymous
ok take ur time
anonymous
  • anonymous
(450x5 + 360 + 2250x10+3600x4 + 1440x)
anonymous
  • anonymous
whats that?
anonymous
  • anonymous
the expanded version of = (45x2) * 2(5x3 + 4) + 2(45x) * (5x3 + 4)2
anonymous
  • anonymous
(45x2) (5x3 + 4)2
anonymous
  • anonymous
became expanded version then that long ans
anonymous
  • anonymous
y did u expand it?
anonymous
  • anonymous
did u check the first derivative?
anonymous
  • anonymous
not supposed to?
anonymous
  • anonymous
but u were gonna do that
anonymous
  • anonymous
hmm.. first derivative = (45x2) (5x3 + 4)2
anonymous
  • anonymous
correct?
anonymous
  • anonymous
it has to be
anonymous
  • anonymous
used chain rule
anonymous
  • anonymous
f''(x)= 90x(5x3 + 4)^2+(45x^2)2(5x^3+4)15x^2
anonymous
  • anonymous
\[90x(5x^3+4)^2 + (675x^3)(5x^3+4)\]
anonymous
  • anonymous
where did u get 15x2 from
anonymous
  • anonymous
it was already simplified in the first derivative
anonymous
  • anonymous
= [(45x2) * 2(5x3 + 4)] + [90x * (5x3 + 4)2]
anonymous
  • anonymous
open that up = [(45x2) * (10x3 + 8)] + [90x * (25x9 + 40x3 + 16)]
anonymous
  • anonymous
open further = = 2250x10 + 450x5 + 3600x4 + 1440x
anonymous
  • anonymous
is that correct?
anonymous
  • anonymous
u know how to apply chain rule?
anonymous
  • anonymous
you said product rule i think thats where i made the mistake
anonymous
  • anonymous
chain rule is again used in product rule
anonymous
  • anonymous
ohhhh
anonymous
  • anonymous
alright let me solve again and brb
anonymous
  • anonymous
ok
anonymous
  • anonymous
[(45x2)*2(5x3 + 4)*15x2] + [90x * 90(5x3 + 4)2]

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