1.

Differntiate the following functions by proper substitution.sin^(-1)((2x)/(1+x^2))

Answer»

Solution :`y=sin^(-1)frac(2x)(1+x^2)`[PUT x=`tantheta`
`sin^(-1)frac(2 TAN theta)(1+tan^2theta)=sin^(-1)sin2theta`
`=2theta=2 tan^(-1)x`
`thereforedy/dx=2/(1+x^2)`


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