What is the derivative of $sqrt( x^2-1)$ ?

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Answer 1 · 2015-12-27T17:09:18

$x/sqrt(x^2-1)$

This is equivalent to $(x^2-1)^(1/2)$ .

According to the chain rule:

$d/dx(u^(1/2))=1/2u^(-1/2) * (du)/dx$

Thus,

$d/dx((x^2-1)^(1/2))=1/2(x^2-1)^(-1/2)d/dx(x^2-1)$

$=>1/(2sqrt(x^2-1)) * 2x$

$=>x/sqrt(x^2-1)$

What is the derivative of sqrt( x^2-1)sqrt( x^2-1)?