How to find the derivative of #3arccos(x/2)#?

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How to find the derivative of #3arccos(x/2)#?

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Answer 1 · 2015-04-16T02:33:03

-#3/[2sqrt(1-x^2/4)]#

Let y= 3 arc cos#x/2#, so that #y/3# = arc cos#x/2#
Thus, cos#y/3#= #x/2# and hence sin#y/3# = #sqrt(1- x^2/4)#
Now differentiate, -#1/3# sin#y/3# #dy/dx# = #1/2#

#dy/dx#= -#3/[2sin(y/3)]#

= -#3/[2sqrt(1-x^2/4)]#

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How to find the derivative of #3arccos(x/2)#?

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