What is the second derivative of (x^2 +5)^4? I've got the answer, but I don't know how to simplify it.... But my answer may be wrong. I got [8x(x^2 +5)^3] + [ 8(x^2 +5)^4]

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions.

- anonymous

- katieb

See more answers at brainly.com

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- anonymous

nah, after the first derivative it looks like your product rule went awry

- anonymous

what did you get for the first derivative?
8x(x^2+5)^3???

- anonymous

I'm not surprised... I'm awful at math. :/
I got 8x(x^2 +5) +8

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- anonymous

Oops, make that 8x(x^2 +5)^3 +8

- anonymous

whoops, wrong thread...

- anonymous

umm, nah everybody struggles with calculus the first go round!

- anonymous

ok, for the first derivative, don't add 8 since it is not a product rule. other than that it looks fine

- anonymous

so y'=8x(x^2+5)^3
now to find y'' take derivative of this and use product rule with the first product being 8x and then the second term of the product being (x^2+5)^3

- anonymous

I got
[8x * 8x(x^2+5)^3] + [8(x^2+5)^4]

- anonymous

But I have to simplify that (assuming that what I have is right, but it's probably not), which is what I can't figure out.
I know that the GCF is 8(x^2+5)^3, and I know that the second half of the equations will be (x^2+5), but the first half is what I don't understand.

- anonymous

derivative of 8x is just 8, so the first term will be 8*(x^2+5)^3
the next term, now instead of differentiating with respect to 8x, you do (x^2+5)^3

- anonymous

which should give you 8x*[6x(x^2+5)^2] or 48x^2(x^2+5)^2

- anonymous

the whole second derivative then will be those two terms added together
8*(x^2+5)^3 +48x^2(x^2+5)^2

- anonymous

But that's not the simplified version, right?

- anonymous

yeah, take out the GCF of 8(x^2+5)^2*[x^2+5+6x^2) and then combine like terms

- anonymous

final answer should be something like
y''= 8(x^2+5)^2*(7x^2+5)

- anonymous

I typed that into my assignment, and it says that should be this
8(x^2+5)^3*(7x^2+5)

- anonymous

hmm, let me double-check, but I don't think so, since the power that is common should have dropped down to 2, not 3

- anonymous

hmm, I got the same answer when I re-did it...I don't know why it is a power of 3 to be honest

- anonymous

I don't, either! :p
Thanks for helping me, though! I really appreciate it! :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.