Differentiate sin^-1 (x/2)?

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Answer 1 · 2018-04-12T15:42:36

#(dy)/(dx)=1/sqrt(4-x^2)#

We know that,

#color(red)(d/(dx)(sin^-1t)=1/sqrt(1-t^2)#

Here,

#y=sin^-1 (x/2)#

Let, #u=x/2,#

#:.y=sin^-1u,where, u=x/2#

#=>(dy)/(du)=1/sqrt(1-u^2) and(du)/(dx)=1/2#

#"Using "color(blue)"Chain Rule"#

#(dy)/(dx)=(dy)/(du) * (du)/(dx)=1/sqrt(1-u^2)*1/2#

#(dy)/(dx)=1/sqrt(1-(x/2)^2)xx1/2#

#=2/sqrt(4-x^2) xx1/2#

#=1/sqrt(4-x^2)#