Care este derivatul lui lnx ^ lnx?

Care este derivatul lui lnx ^ lnx?
Anonim

Răspuns:

# = 2 (ln x) / x #

Explicaţie:

# (LNX ^ LNX) ^ '#

# = (ln x lnx) ^ '#

# = (ln ^ 2 x) ^ '#

# = 2 ln x * 1 / x #

Răspuns:

# LNX ^ (LNX) * (ln (LNX) +1) / x #

Explicaţie:

# Y = LNX ^ (LNX) = e ^ (ln (LNX ^ (LNX)) #

# (Y) '= (e ^ (ln (LNX ^ (LNX))))' # #=#

# E ^ (ln (LNX ^ (LNX))) * (ln (LNX ^ (LNX))) "# #=#

# LNX ^ (LNX) * (LNX (ln (LNX)) "# #=#

# LNX ^ (LNX) * (ln (LNX) / x + LNX * 1 / LNX (LNX) ') # #=#

# LNX ^ (LNX) * (ln (LNX) / x + anula (LNX) * 1 / (xcancel (LNX))) # #=#

# LNX ^ (LNX) * (ln (LNX) +1) / x #