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If y= (sinx -cos x )^((sin x +cos x ) )...

If ` y= (sinx -cos x )^((sin x +cos x ) ),then (dy)/(dx)=`

A

` y(((sin x+cos x )^(2))/( sin x-cos x )+ (cosx -sinx )log (sinx -cos x ) )`

B

` y(((sin x+cos x )^(2))/( sin x-cos x )- (cosx -sinx )log (sinx -cos x ) )`

C

` y((sin x+cos x )/( sin x-cos x )+ (cosx -sinx )log (sinx -cos x ) )`

D

` y((sin x+cos x )/( sin x-cos x )- (cosx -sinx )log (sinx -cos x ) )`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • If y= (sin x + cos x)/( sin x- cos x) , find (dy)/(dx) .

    A
    `(2)/( ( sin x- cos x)^2)`
    B
    `(-2)/( (sin x - cosx)^2)`
    C
    `(-2)/( (sinx + cos x)^2)`
    D
    None of these

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

    A
    `(sin^2 (a+y))/(sin a)`
    B
    `( cos a)/( cos^2 (a +y))`
    C
    `(cos^2 (a+y))/(cos a)`
    D
    None

  • If y=cos (sin x ),then (dy)/(dx) =

    A
    ` (sin x ) sin (sin x ) `
    B
    ` -(sinx ) sin (sin x) `
    C
    ` (cos x )sin (sin x) `
    D
    ` -(cos x )sin ( sin x ) `

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