Question

Question about derivative of
ln(x*sqrt(x^2-6)

Would it be derivative of
lnx + lnsqrt(x^2-6)
which would be 1/x + (1/2) (1/sqrtx^2-6) (2x)

Answer 1

i think so

Answer 2

\[\ln(x\sqrt{x^2-6})=\ln(x)+\frac{1}{2}\ln(x^2-6)\]

Answer 3

taking derivatives gives
\[\frac{1}{x}+\frac{x}{x^2-6}\]

Answer 4

I'm getting confused with x/x^2-6

Answer 5

wouldn't it be 1/sqrtx^2-6