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7 January, 03:15

Find dy/dx if y = (cos x) ^ x

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  1. 7 January, 03:33
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    Y = (cos x) ^x

    log y = log (cos x) ^x = x log (cos x)

    1/y dy/dx = x * 1/cos x * - sin x + log (cos x) = - xsin x / cos x + log (cos x) = log (cos x) - xtan x

    dy/dx = y (log (cos x) - xtan x) = (cos x) ^x (log (cos x) - xtan x)
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