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  • Differentiate w.r.to x cot^-1 ( 3- 2tan x / 2+ 3tan x)

Differentiate w.r.to x cot^-1 ( 3- 2tan x / 2+ 3tan x)

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Solution:   Let  

                    y=cot ^-1(frac3-2 an x2+3 an x)= an^-1(frac2+3 an x3-2 an x)

             Rightarrow      y= an^-1[fracfrac23+ an x1-(frac23) an x]= an^-1frac23+ an^-1( an x)

               Differentiate w.r.to x we get

              herefore                                      fracmathrmd ymathrmd x=0+1=1.

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Deependra Verma

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