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Question
Differentiate the following w.r.t. x:
`cos x/log x`, x > 0
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Solution
Let, y = `cos x/log x`
Differentiating both sides with respect to x,
`dy/dx = d/dx cos x/log x`
= `(log x d/dx cos x - cos x d/dx log x)/(log x)^2`
= `(log x (- sin x) - cos x xx 1/x)/((log x)^2)`
= `(- sin x log x - cos x/x)/(log x)^2`
= `(- (x sin x log x + cos x))/(x (log x)^2)`, x > 0
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