Maharashtra State BoardHSC Commerce 12th Board Exam
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Find dydx, if y = xx. - Mathematics and Statistics

Sum

Find `"dy"/"dx"`, if y = xx.

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Solution

y = xx.

Taking logarithm of both sides, we get

log y = log (xx)

∴ log y = x log x

Differentiating both sides w.r.t.x, we get

`1/"y" * "dy"/"dx" = "x" * "d"/"dx" (log "x") + log "x" * "d"/"dx" ("x")`

`= "x" * 1/"x" + log "x" (1)`

∴ `1/"y" * "dy"/"dx" = 1 + log x`

∴ `"dy"/"dx" = "y"(1 + log "x")`

∴ `"dy"/"dx" = "x"^"x" (1 + log "x")`

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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 3 Differentiation
Miscellaneous Exercise 3 | Q 4.06 | Page 100
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