Question

Simplify the function f(t) = sinh(ln(t)). Then, find the derivative of your simplified form of f(t).

Answer 1

Hi ScottHann :)

I think it is much easy.

Answer 2

f(t)= t/2 - 1/2t

Answer 3

Sinh is the same as (e^x-e^-x)/2 and as we know from properties of logarithms e^lnx=x

Answer 4

f'(t)= 1/2 + 1/2t^2

Answer 5

\[\Large\sinh=\frac{e^x-e^{-x}}{2}\]
If \[\large x=ln(t)\]
then\[\large e^x=t\] and \[\large e^{-x}=1/t\]
So
\[\Large sinh=\frac{t-1/t}{2}\]
Now I think you can simplify it more.

Answer 6

Shayaan_Mustafa is right.

Answer 7

I have forgotten to use complete it should be look like this
\[\Large sinh(lnt)=\frac{t-1/t}{2}\]

Answer 8

I forgot to use argument.

Answer 9

Shayaan, thanks. I came up with (t^2-1)/2t, and Web Assign said it was wrong.

Answer 10

Well OK. Good luck.

Answer 11

Thanks.

Answer 12

Shayaan, thanks for your help. Your answer was correct.