If y= 2 ^(sin x) -sin ^(2)x ,then (dy)/...

If ` y= 2 ^(sin x) -sin ^(2)x ,then (dy)/(dx) =`

A

` (2sin ^(x) log 2-2 sin x ) (cos x) `

B

` (2sin ^(x) log 2- sin x ) (cos x) `

C

` -(2sin ^(x) log 2-2 sin x ) (cos x) `

D

` -(2sin ^(x) log 2- sin x ) (cos x) `

Text Solution

Verified by Experts

The correct Answer is:

A

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If y= x^(sin x) +(sin x)^(x) ,then (dy)/(dx) =

A

` x^(sinx ) ((cosx )( log x) -(sin x)/( x )) + (sin x)^(x) (log sin x -xcot x ) `

B

` x^(sinx ) ((cosx )( log x) +(sin x)/( x )) + (sin x)^(x) (log sin x +xcot x ) `

C

` x^(sinx ) ((cosx )( log x) -(sin x)/( x )) - (sin x)^(x) (log sin x +xcot x ) `

D

` x^(sinx ) ((cosx )( log x) +(sin x)/( x )) + (sin x)^(x) (log sin x -xcot x ) `

If sin y=x sin (a +y) , then (dy)/(dx)=

A

`( sin^2 ( a +y))/(sin a)`

B

` sin (a +y)`

C

`sin^2 (a+y)`

D

` (sin (a+ y))/( sin a)`

If y =sin (x^(2) +x) ,then (dy)/(dx) =

A

` -(2x +1) cos (x^(2) +x) `

B

` (2x +1)cos (x^(2) +x) `

C

`2xcos (x^(2) +5) `

D

` (2x+ 5)cos (x^(2) +5)`

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