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Question
Find the derivatives of the following:
(cos x)log x
Solution
y = (cos x)log x
Taking log on both sides
log y = log (cos x)log x
log y = (log x) log (cos x)
Differentiating with respect to x
`1/y * ("d"y)/("d"x) = log x xx 1/cosx xx - sin x + log(cosx) xx 1/x`
`1/y ("d"y)/("d"x) = - tan x (log x) + (log(cosx))/x`
`("d"y)/("d"x) = y [(log(cos x))/x - tan x (log x)]`
`("d"y)/("d"x) = (cos x)^(logx) [(log(cos x))/x - tan x (log x)]`
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