Question

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]

Answer 1

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

Answer 2

what did you get for the first derivative?

8x(x^2+5)^3???

Answer 3

I'm not surprised... I'm awful at math. :/

I got 8x(x^2 +5) +8

Answer 4

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

Answer 5

whoops, wrong thread...

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

I got

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

Answer 10

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.

Answer 11

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

Answer 12

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

Answer 13

the whole second derivative then will be those two terms added together

8*(x^2+5)^3 +48x^2(x^2+5)^2

Answer 14

But that's not the simplified version, right?

Answer 15

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

Answer 16

final answer should be something like

y''= 8(x^2+5)^2*(7x^2+5)

Answer 17

I typed that into my assignment, and it says that should be this

8(x^2+5)^3*(7x^2+5)

Answer 18

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

Answer 19

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

Answer 20

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