Question #b7cd0

Question

1281 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-19T18:02:18

$dy/dx=1/(2sqrt(x(1-x)$

$"Let"y=sin^-1(sqrtx)$

$dy/dx=?$

$u=sqrtx$

$u^2=x$

$(du)/dx=1/(2sqrtx)$

$y=sin^-1u$

$(dy)/(du)=1/sqrt(1-u^2)$

$(dy)/(du)=1/sqrt(1-x)$

$dy/dx=dy/(du)(du)/dx$

$dy/dx=1/sqrt(1-x)xx1/(2sqrtx)=1/(2sqrt(x(1-x)$

$dy/dx=1/(2sqrt(x(1-x)$