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प्रश्न
Solve the following:
If y = [log(log(logx))]2, find `"dy"/"dx"`
उत्तर
y = [log(log(logx))]2
Differentiating both sides w.r.t. x, we get
`"dy"/"dx" = "d"/"dx" [log(log(log "x"))]^2`
`= 2[log(log(log "x"))] xx "d"/"dx" [log(log(log "x"))]`
`= 2[log(log(log "x"))] xx 1/(log(log "x")) xx "d"/"dx" [log(log "x")]`
`= 2[log(log(log "x"))] xx 1/(log(log "x")) xx 1/(log "x") xx "d"/"dx" (log "x")`
`= 2[log(log(log "x"))] xx 1/(log(log "x")) xx 1/(log "x") xx 1/"x"`
∴ `"dy"/"dx" = (2[log(log(log "x"))])/("x"(log "x")(log (log "x")))`
Notes
The answer in the textbook is incorrect.
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