Question

 If `"y" ="x"^"x" , "find"  "dy"/"dx"`.

Answer 1

`"y" ="x"^"x"`                                     ......(1)
Taking log on both sides,
log y = log X^x
logy  =x log x
Differentiate both sides w.r.t x
`1/"y" . "dy"/"dx" = ("x" xx 1)/"x" + log "x" xx 1`

`"dy"/"dx" = "y"[1 + log "x"]`

=X^x [ 1+ log x] from (1)