كيف يمكنك التمييز بين sqrt ((x + 1) / (2x-1))؟

إجابة:

# - (3 (x + 1)) / (2 (2x-1) ^ 2 sqrt ((x + 1) / (2x-1)) #

تفسير:

#f (x) = u ^ n #

#f '(x) = n xx (du) / dx xxu ^ (n-1) #

في هذه الحالة:# sqrt ((x + 1) / (2x-1)) = ((x + 1) / (2x-1)) ^ (1/2): #

# n = 1/2 ، u = (x + 1) / (2x-1) #

# d / dx = 1/2 xx (1xx (2x-1) - 2xx (x + 1)) / (2x-1) ^ 2 xx ((x + 1) / (2x-1)) ^ (1 / 2-1) #

# = 1 / 2xx (-3) / ((2x-1) ^ 2 xx ((x + 1) / (2x-1)) ^ (1 / 2-1) #

# = - (3 (x + 1)) / (2 (2x-1) ^ 2 ((x + 1) / (2x-1)) ^ (1/2) #