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Show that (dy)/(dx)=sec x. If y=(log)sqr...

Show that `(dy)/(dx)=sec x`. If `y=(log)sqrt((1+sinx)/(1-sinx))`

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The correct Answer is:
2
`y=log sqrt((1+ sin x)/(1- sin x))=(1)/(2)[log_(e)(1+ sin x) -log _(e) (1- sin x)]`
`therefore" "(dy)/(dx)=(1)/(2){(1)/(1+ sin x dx)(d)/(dx)(1+ sin x)-(1)/(1- sin x )(d)/(dx)(1- sin x )}`
`=(1)/(2){(cos x)/(1+ sin x)+(cos x )/(1-sin x)}`
`=(1)/(2)cos x ((2)/(1- sin^(2)x))=(cos x)/(cos^(2)x)=sec x`
`"or "(dy)/(dx):|_(x=(pi)/(3))=sec""(pi)/(3)=2`
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