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