Question

simplify f(x)=ln((e^x sqroot (x^2+1))/(x-2)^3)

Answer 1

You can write that as:
\[f(x)=\ln(e^x \sqrt{x^2+1})-\ln((x-2)^3)=\ln(e^x)+\ln((x^2+1)^{1/2})-\ln((x-2)^3)\]
From here:
\[f(x)=x+(1/2)\ln(x^2+1)-3\ln(x-2)\]

Answer 2

omg do you know how to do f'(x)

Answer 3

Well, to differentiate that. Go left to right.
\[f'(x)=1+(1/2)(2x/(x^2-1))-3/(x-2)\]
Since d/dx(ln(x))=1/x

Answer 4

easy once you simplify the log. may want to write middle term as
\[\frac{x}{x^2-1}\]

Answer 5

mv, how come your latex looks so much nicer than mine?

Answer 6

Exactly^^ That comes from multiplying the (1/2) by 2x which leaves you with just an x in the numerator. I have no idea D: I'm fairly new here. o.o

Answer 7

wait the answer is only x

Answer 8

Nah, its what I have. Satellite was just point out that you could simplify it a little.