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Differentiate (cosx)^(sinx) w.r.t (sinx)...

Differentiate `(cosx)^(sinx)` w.r.t `(sinx)^(cosx)`

A

` ((sin x)^(cos x) (cos x cot x -sin x log (sin x )))/( (cos x ) ^(sin x) (cos x log (cosx ) -sin xtanx ))`

B

` (-(sin x)^(cos x) (cos x cot x -sin x log (sin x )))/( (cos x ) ^(sin x) (cos x log (cosx ) -sin xtanx ))`

C

`( (cos x ) ^(sin x) (cos x log (cosx ) -sin xtanx )) /(-(sin x)^(cos x) (cos x cot x -sin x log (sin x )))`

D

`(- (cos x ) ^(sin x) (cos x log (cosx ) -sin xtanx )) /((sin x)^(cos x) (cos x cot x -sin x log (sin x )))`

Text Solution

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The correct Answer is:
C
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