I have trouble finding the second derivative, my answer is a little off from the answer key.

Question

f(x)=(log(base2)x)^5
f'(x)=[5(log(base2)x)^4]/xln2
f"(x)=[20(log(base2)x)³(xln2)-(ln2+(x/2))(5(log(base2)x)^4)]/[x²(ln2)²]

for the f"(x), is g(x)=xln2? It is a product so I think it should be dealt with differently, but I am unclear on that.

Thanks

Answer 1

in your f ''(x) you forgot to differentiate the log₂x part , and in the second part when you differentiate xln2 you simply get ln2.
Remember ln2 is just a number so xln2 is (ln2)x , a simple term like 6x.

I had

f ''(x) = [20(log(base2)x)³(1/(xln2)(xln2)-(ln2))(5(log(base2)x)^4)]/[x²(ln2)²]

Now doesn't the xln2 at the top and bottom of the first section cancel?
check my arithmetic, too early in the morning

Answer 2

I have the same thing now, thanks! I thought I had to use product rule for xln2, but there's no variable in ln2, so it is accounted for a constant?