What is the derivative of $arcsin (\frac{2 x}{1 + x^{2}})$ $arcsin((2x)/(1+x^2))$ ?

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Answer 1 · 2016-07-07T09:29:41

$\frac{2}{1 + x^{2}}$ $2/(1+x^2)$

' means differentiation with respect to x.

Let $x = tan (\frac{θ}{2})$ $x=tan(theta/2)$ . Then, $theta=2tan^(-1)x and theta'=2/(1+x^2)$ .

Now, $(arc sin ( (2x)/(1+x^2) )'$

$=(arc sin ( ( 2 tan (theta / 2) )/( 1+tan^2(theta/2))))'$

$=(arc sin (sin theta))'$

$=theta'$

$=2/(1+x^2)$ .

What is the derivative of arcsin((2x)/(1+x^2))arcsin(2x1+x2)arcsin((2x)/(1+x^2))?