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

1. calyne

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