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Question

If y=logsinx2,0<x<π2, then dydxat x=π2 is


A

0

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B

1

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C

π4

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D

π

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Solution

The correct option is D

π


Find the dydx:

Given that, y=logsinx2,0<x<π2

Differentiate y with respect to x.

dydx=1sinx2cosx22x=2xcotx2
Put x=π2
dydx=2(π2)cotπ4=π \\
Hence option D is correct.


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