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