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Question
Find the second order derivative of the function.
sin (log x)
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Solution
Let, y = sin (log x)
Differentiating both sides with respect to x,
`dy/dx = d/dx sin (log x)`
= `cos (log x) d/dx log x`
= `cos (log x) * 1/x`
= `(cos (log x))/x`
Differentiating both sides again with respect to x,
`d/dx [dy/dx] = d/dx [(cos (log x))/x]`
`(d^2y)/dx^2 = (x d/dx cos (log x) - cos (log x) d/dx (x))/x^2`
= `(x [-sin (log x)] * 1/x - cos (log x * 1))/x^2`
= `(-[sin (log x) + cos (log x)])/x^2`
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