Mikä on yhtälö f (x) = e ^ x / lnx-x: n tangenttilinjasta x = 4?

Vastaus:

# Y = (e ^ 4 / LN4-e ^ 4 / (4ln ^ 2 (4)) - 1) x-4 + e ^ 4 / ln4-4 (e ^ 4 / LN4-e ^ 4 / (4ln ^ 2 (4)) - 1) #

Selitys:

#f (x) = e ^ x / lnx-x #, # D_f = (0,1) uu (1, + oo) #

#f '(x) = (e ^ xlnx-e ^ x / x) / (lnx) ^ 2-1 = #

# (E ^ x (xlnx-1)) / (x (lnx) ^ 2) -1 = #

# E ^ x / lnx-e ^ x / (xlnA ^ 2x) -1 #

Tangenttilinjan yhtälö kohdassa #M (4, f (4)) # tulee olemaan

# Y-f (4) = f '(4) (x-4) # #<=>#

# Y-e ^ 4 / LN4 + 4 = (e ^ 4 / LN4-e ^ 4 / (4ln ^ 2 (4)) - 1) (x-4) = #

# Y = (e ^ 4 / LN4-e ^ 4 / (4ln ^ 2 (4)) - 1) x-4 + e ^ 4 / ln4-4 (e ^ 4 / LN4-e ^ 4 / (4ln ^ 2 (4)) - 1) #