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

- anonymous

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

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- anonymous

step by step please

- anonymous

I assume that the 3 is a power?

- anonymous

well i used chain rule

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## More answers

- anonymous

f'(x)=3(5x3 + 4)^2[15x^2]

- anonymous

[45(x2)](2)(5x3 +4)1(15x3-1) + (45x2) (5x3 + 4)2

- anonymous

\[45(5x^3+4)(x^2)\]

- anonymous

oh again missed the exponent 2

- anonymous

is my first step corrrect

- anonymous

\[f'(x)=45(5x^3+4)^2(x^2)\]

- anonymous

(45x2) (5x3 + 4)2

- anonymous

3 is not in power?

- anonymous

right, now how to do second derivative

- anonymous

use product rule

- anonymous

F(x) = (5x^3 + 4)^2

- anonymous

is the questions

- anonymous

wait your derivative doesnt seem right

- anonymous

this is not the same u posted earlier

- anonymous

oh no
its to the third power

- anonymous

but the way you wrote the answer is different

- anonymous

(45x^2) (5x3 + 4)2 by using chain rule

- anonymous

then the derivative is correct:)

- anonymous

right

- anonymous

now use the product rule

- anonymous

you left the 45 and x^2 separately

- anonymous

confused me

- anonymous

y confused?

- anonymous

45(5x3+4)(x2)

- anonymous

how can you separate 45 from the equation

- anonymous

this is the second step, read the first too

- anonymous

y seperated? it is being multiplied

- anonymous

ok let me me work it out and see if our answers match

- anonymous

ok take ur time

- anonymous

(450x5 + 360 + 2250x10+3600x4 + 1440x)

- anonymous

whats that?

- anonymous

the expanded version of = (45x2) * 2(5x3 + 4) + 2(45x) * (5x3 + 4)2

- anonymous

(45x2) (5x3 + 4)2

- anonymous

became expanded version then that long ans

- anonymous

y did u expand it?

- anonymous

did u check the first derivative?

- anonymous

not supposed to?

- anonymous

but u were gonna do that

- anonymous

hmm.. first derivative = (45x2) (5x3 + 4)2

- anonymous

correct?

- anonymous

it has to be

- anonymous

used chain rule

- anonymous

f''(x)= 90x(5x3 + 4)^2+(45x^2)2(5x^3+4)15x^2

- anonymous

\[90x(5x^3+4)^2 + (675x^3)(5x^3+4)\]

- anonymous

where did u get 15x2 from

- anonymous

it was already simplified in the first derivative

- anonymous

= [(45x2) * 2(5x3 + 4)] + [90x * (5x3 + 4)2]

- anonymous

open that up = [(45x2) * (10x3 + 8)] + [90x * (25x9 + 40x3 + 16)]

- anonymous

open further = = 2250x10 + 450x5 + 3600x4 + 1440x

- anonymous

is that correct?

- anonymous

u know how to apply chain rule?

- anonymous

you said product rule i think thats where i made the mistake

- anonymous

chain rule is again used in product rule

- anonymous

ohhhh

- anonymous

alright let me solve again and brb

- anonymous

ok

- anonymous

[(45x2)*2(5x3 + 4)*15x2] + [90x * 90(5x3 + 4)2]

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