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If y= Tan^(-1) (sin sqrtx) + Cosec^(-1) ...

If `y= Tan^(-1) (sin sqrtx) + Cosec^(-1) (e^(2x+1))` then `(dy)/(dx)=`

A

`(1)/(sqrtx ( 1+ sin^2 sqrtx))`

B

`(cos sqrt(x))/(2 sqrtx (1+ sin^2 sqrtx))-(2)/(e^(4x+2)-1)`

C

`(cos sqrtx)/((1+ sin^2 sqrtx))+(2)/(sqrt(e^(4x+2)+1))`

D

`(1)/(2 sqrtx) (cos sqrtx)/((1+ sin^2 sqrtx)) - (2)/(sqrt(e^(2x+1)-1))`

Text Solution

Verified by Experts

The correct Answer is:
B
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