Hello,
(tg(x))'=1/cos²(x)
(arcsin(x))'=1/√(1-x²)
cos²(arcsin(x))=1-sin²(arcsin(x))=1-x²
[tex](tg(arcsin(x)))'= \dfrac{1}{cos(arcsin(x)))^2} * \dfrac{1}{\sqrt{1-x^2}} \\
=\dfrac{1}{1-sin(arcsin(x))^2}* \dfrac{1}{\sqrt{1-x^2}} \\
= \dfrac{1}{1-x^2} * \dfrac{1}{\sqrt{1-x^2}} \\
\boxed{= \dfrac{\sqrt{1-x^2}}{x^4-2x^2+1}}\\
[/tex]
