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Y=tan-1((x-1)/(x+1))
Dy/dx=[1/{1+((x-1)/(x+1))2}].[(x+1).1-(x-1).1]/(x+1)2
=[1/{(x+1)2+(x-1)2}].2
=2/2(x2+1)=1/(1+x2)
Let z=sin-1(3x-4x3)
=3sin-1x
Dz/dx=3/v(1-x2)
Then dy/dz=(dy/dx)/(dz/dx)={1/(1+x2)}/{3/v(1-x2)}
=v(1-x2)/3(1+x2) Ans.
Thanks & Regards
Rinkoo Gupta
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