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How do you find the derivative of #arcsin (x/2)#?

1 Answer

Jun 30, 2017

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

Explanation:

The derivative of #arcsinu#:

#d/dx(arcsinu)=(u')/sqrt(1-u^2)#

#therefored/dx(arcsin(x/2))=((x/2)')/sqrt(1-(x/2)^2)=(1/2)/sqrt(1-x^2/4)#
#=1/(2sqrt((4-x^2)/4))=1/sqrt(4-x^2)#

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