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Question
Differentiate the following w.r.t. x:
`cos x/log x, x >0`
Solution
Let, y = `cos x/log x, x > 0`
Differentiating both sides with respect to x,
`dy/dx = (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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