How do you use logarithmic differentiation to find the derivative of y = (cos x)^lnx
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How do you use logarithmic differentiation to find the derivative of y = (cos x)^lnx

[From: ] [author: ] [Date: 11-11-07] [Hit: ]
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y = (cos x)^(ln x)

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

Differentiating both sides:

y'/y = -ln(x)*tan(x) + ln(cos(x))/x

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