Bagaimana anda mencari derivatif kedua ln (x ^ 2 + 4)?

Jawapan:

# (d ^ 2ln (x ^ 2 + 4)) / dx ^ 2 = (8 - 2x ^ 2) / (x ^ 2 + 4) ^ 2 #

Penjelasan:

Peraturan rantai adalah:

# (d {f (u (x))}) / dx = (df (u)) / (du) ((du) / dx) #

Biarkan #u (x) = x ^ 2 + 4 #, kemudian # (df (u)) / (du) = (dln (u)) / (du) = 1 / u # dan # (du) / dx = 2x #

# (dln (x ^ 2 + 4)) / dx = (2x) / (x ^ 2 + 4) #

# (d ^ 2ln (x ^ 2 + 4)) / dx ^ 2 = (d ((2x) / (x ^ 2 + 4))) / dx #

# (d ((2x) / (x ^ 2 + 4))) / dx = #

# {2 (x ^ 2 + 4) - 2x (2x)} / (x ^ 2 + 4) ^ 2 = #

# (8 - 2x ^ 2) / (x ^ 2 + 4) ^ 2 #