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If y=(xsinx+cosx)(xcosx-sinx) then find ...

If `y=(xsinx+cosx)(xcosx-sinx)` then find `dy/dx`

Text Solution

Verified by Experts

`y =(xsinx+cosx)(xcosx-sinx)`
`dy/dx = (xcosx+sinx-sinx)(xcosx-sinx)+(xsinx+cosx)(-xsinx+cosx-cosx)`
`=>dy/dx= (xcosx)(xcosx-sinx)+(xsinx+cosx)(-xsinx)`
`=>dy/dx= x^2cos^2x-xcosxsinx-x^2sin^2x-xsinxcosx`
`=>dy/dx= x^2(cos^2x-sin^2x) -2xsinxcosx`
`=>dy/dx= x^2cos2x-xsin2x`
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Knowledge Check

  • If y=tan^(-1)[(sinx+cosx)/(cosx-sinx)] then (dy)/(dx) is

    A
    `1/2`
    B
    `(pi)/4`
    C
    0
    D
    1

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