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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)#