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Question
Differentiate the following w.r.t.x: `log_(e^2) (log x)`
Solution
Let y = `log_(e^2) (log x)`
∴ y = `log (log x)/(log e^2) ...[∴ log_b a = (log a)/(log b)]`
∴ y = `log (log x)/(2 log e) ...[∴ log x^a = alog x]`
∴ y = `log (log x)/(2) ...[∴ log e = 1]`
Differentiating w.r.t.x, we get,
`"dy"/"dx" = 1/2 "d"/"dx" log (log x)`
`"dy"/"dx" = 1/2 × 1/(log x). "d"/"dx" (log x)`
`"dy"/"dx" = 1/2 × 1/(log x). 1/x`
`"dy"/"dx" = 1/(2x(log x))`
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