How do you find the derivative of $\sqrt{\frac{x^{2} - 1}{x^{2} + 1}}$ $sqrt((x^2-1) / (x^2+1))$ ?

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Answer 1 · 2015-09-12T22:58:52

It is $f'(x)=(2x)/((sqrt(x^2-1))*(x^2+1)^(3/2))$

We have that

$f(x)=sqrt((x^2-1)/(x^2+1))$ hence

$f'(x)=1/2*1/(sqrt((x^2-1)/(x^2+1)))*((x^2-1)/(x^2+1))'$

$f'(x)=1/2*sqrt(x^2+1)/sqrt(x^2-1)*((2x(x^2+1)-(x^2-1)2x)/(x^2+1))$

$f'(x)=1/2*sqrt(x^2+1)/sqrt(x^2-1)*(4x/(x^2+1)^2)$

$f'(x)=(2x)/((sqrt(x^2-1))*(x^2+1)^(3/2))$

How do you find the derivative of sqrt((x^2-1) / (x^2+1))√x2−1x2+1sqrt((x^2-1) / (x^2+1))?