Posted by **sh** on Saturday, October 30, 2010 at 5:46am.

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 -
**Reiny**, Saturday, October 30, 2010 at 8:05am
in your f ''(x) you forgot to differentiate the log_{2}x 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 -
**sh**, Saturday, October 30, 2010 at 2:45pm
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?

## Answer This Question

## Related Questions

- Calculus - Find the second derivative of the following function: y=log(base2)x/x...
- Precalculus-Verify - log(base2)x-log(base2)6= log(base2)5+ 2log(base2)3 log(x/6...
- Algebra - In the logarithmic expression . . . log(base 4) 8 , how does the base ...
- Algebra 2 - How would I solve the equation: log(base2)4 - log(base2)(x+3) = log(...
- math - Given that 2 log base2 (x+15) - log base2 x = 6 1.Show that x^2 -34x +225...
- Algebra 2 - solve the equation: log(base2)^(x-3)log(base2)^5 = 2log(base2)^10 I ...
- Math 12 - 7. Simplify. b) log base2 20 + log base3 8 + log base2 3 + log base3 4...
- Math - Evaluate log(base2)8-log(base2)12+log(base2)6
- Pre-Cal - log base2 5 square root of 512 use the definition of b^1/n log base2 ...
- Advanced Functions/ Precalculus Log - 1. Evaluate 4^(log base4 64) + 10^(log100...

More Related Questions