What is derivative of #(arcsin(x))^(2)#?

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Answer 1 · 2015-04-23T20:14:31

#y=(arcsinx)^2#

#y^(1/2)=arcsinx#

#ln(y^(1/2))=ln(arcsinx)#

#1/2*lny=ln(arcsinx)#

#1/2*1/y*(dy)/(dx)=1/(arcsinx*sqrt(1-x^2))#

#2y*1/(2y)*(dy)/(dx)=2y*1/(arcsinx*sqrt(1-x^2))#

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

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