Odgovor:
# d / dx (sin ^ -1 csc (4x)) = 4 * sec 4x * sqrt (1-csc ^ 2 4x) #
Pojasnilo:
Uporabljamo formulo
# d / dx (sin ^ -1 u) = (1 / sqrt (1-u ^ 2)) du #
# d / dx (sin ^ -1 csc (4x)) = (1 / sqrt (1- (csc 4x) ^ 2)) d / dx (csc 4x) #
# d / dx (sin ^ -1 csc (4x)) = (1 / sqrt (1-csc ^ 2 4x)) * (- csc 4x * cot 4x) * d / dx (4x) #
# d / dx (sin ^ -1 csc (4x)) = ((- - csc 4x * cot 4x) / sqrt (1-csc ^ 2 4x)) * (4) #
# d / dx (sin ^ -1 csc (4x)) = ((- 4 * csc 4x * cot 4x) / sqrt (1-csc ^ 2 4x)) * (sqrt (1-csc ^ 2 4x) / (sqrt (1-csc ^ 2 4x))) #
# d / dx (sin ^ -1 csc (4x)) = ((- 4 * csc 4x * cot 4x * sqrt (1-csc ^ 2 4x)) / (- cot ^ 2 4x)) #
# d / dx (sin ^ -1 csc (4x)) = 4 * sec 4x * sqrt (1-csc ^ 2 4x) #
Bog blagoslovi …. Upam, da je razlaga koristna.
