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If y=sin^(-1)(3x)+sec^(-1)((1)/(3x)), fi...

If `y=sin^(-1)(3x)+sec^(-1)((1)/(3x)),` find `(dy)/(dx)`.

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`t=sin^(-1)(3x)+sec^(-1)((1)/(3x))`
`y=sin^(-1)(3x)+cos^(-1)(3x)(because sin^(-1).(1)/(x)=cos^(-1)x)`
`y=(pi)/(2)" "(because sin^(-1)x+cos^(-1)x=pi//2)`
Differentiating w.r.t. x, we get
`(dy)/(dx)=0`
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