F(x) = (5x3 + 4)3 find the second derivative

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F(x) = (5x3 + 4)3 find the second derivative

Mathematics
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step by step please
I assume that the 3 is a power?
well i used chain rule

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

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