Question

Differentiate the function g(x) = ln[x(sqrt(x^2 - 1))]

Answer 1

and SIMPLIFY THE ANSWER

Answer 2

i got up to g'(x) = 1/x + 1/[2(x+1)] + 1/[2(x-1)] i can't simplify it i'm retarded help me

Answer 3

We have

\[ g(x)= \ln( x \sqrt { x^2-1})\]
\[g'(x)= \frac{1}{ x\sqrt {x^2-1} } \times ( \sqrt { x^2-1} + x \times \frac{2x}{2 \sqrt {x^2-1}}) \]
or

\[g'(x)= \frac{1}{ x\sqrt {x^2-1} } \times ( \sqrt { x^2-1} + x \times \frac{x}{ \sqrt {x^2-1}}) \]
simplifying now
\[g'(x)= \frac{1}{ x\sqrt {x^2-1} } \times ( \frac{x^2-1+x^2}{ \sqrt {x^2-1}}) \]

\[g'(x)= \frac{2x^2-1}{ x( x^2-1)} \]