## calyne 3 years ago Differentiate the function g(x) = ln[x(sqrt(x^2 - 1))]

1. calyne

2. calyne

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

3. ash2326

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 $g'(x)= \frac{1}{ x\sqrt {x^2-1} } \times ( \frac{x^2-1+x^2}{ \sqrt {x^2-1}})$ $g'(x)= \frac{2x^2-1}{ x( x^2-1)}$