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

Question

anonymous · Answer

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:
$$f(x)=x+(1/2)\ln(x^2+1)-3\ln(x-2)$$

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

wait the answer is only x

anonymous · Answer

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