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11 August, 02:23

Find the derivative of f (x) = 4.15cos^x

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  1. 11 August, 03:44
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    Did you mean the derivative of (cos x) ^x? Then, use logarithmic differentiation:

    y = (cos x) ^x

    ln (y) = ln[ (cos x) ^x]

    ln (y) = x * ln[cos x]

    (1/y) * y' = 1 * ln[cos x] + x * (-sin x) / (cos x)

    y' / y = ln[cos x] - (x sin x) / (cos x)

    y' = y * [ ln[cos x] - (x sin x) / (cos x) ]

    the key step in the process - the substitution.

    You had: y = (cos x) ^x, so we will substitute for y.

    y' = (cos x) ^x * [ ln[cos x] - (x sin x) / (cos x) ]

    (and this is your final answer)
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