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Calculus

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

  • Calculus -

    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

  • Calculus -

    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?

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