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

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Mathematics

Alexandria Fields

20 January, 13:28

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

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Johnny · Answer 1

G (x) = ln[x (sqrt (x^2 - 1)) ]

g' (x) = 1/[x (sqrt (x^2 - 1)) ] * (x^2/sqrt (x^2 - 1) + sqrt (x^2 - 1)) = ((x^2 + x^2 - 1) / sqrt (x^2 - 1)) / x (sqrt (x^2 - 1)) = (2x^2 - 1) / x (x^2 - 1) = (2x^2 - 1) / (x^3 - x)