calculus question

Question

Whats the derivative of (8^(2t))/t? (Hint: In some exercises, you may find it helpful to apply logarithmic properties before differentiating.)

the answer is (9ln(2) * (512^t) * t - 512^t)/t^2 but i don't know how to do it

Answer 1

Hi Ashy,

If I am understanding this problem correctly. I am letting x = ( 8^2t ) / t

When I solved this problem I did not get the answer you stated so I am not sure if I am understanding the problem correctly.

To solve this problem:

step 1. take the log of each side, or Ln

step 2. apply division property of logs( log(numerator) - log(denominator))

step 3. apply log property of exponents

step 4. I prefer to undo the log step exponentiating

step 5. then take the derivative (here I have a constant and 1 e^t term)

I hope I interpreted the question correctly because I did not get the answer you stated. I hope this helps. Let me know if you have more questions.