Class 12th Calculus

If y = e^x cosx, prove that dy/dx sqrt(2) e^x . cos(x+ pie/4)

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  1. The simple dy/dx = e^x(-sinx) + e^xcosx
    = e^x(cosx - sinx)

    RS = √2(e^x)(cos(x+π/4)
    = √2(e^x)(cosxcosπ/4 - sinxsinπ/4)
    = √2(e^x)(cosx(1/√2 - sinx(1/√2)
    = e^x (cosx - sinx)

    = the dy/dx from above

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