Svar:
# d / dx (sin ^ -1 csc (4x)) = 4 * sek 4x * sqrt (1-csc ^ 2 4x) #
Forklaring:
Vi bruger formlen
# 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 * barneseng 4x) * d / dx (4x)
# d / dx (sin ^ -1 csc (4x)) = ((- csc 4x * barneseng 4x) / sqrt (1-csc ^ 2 4x)) * (4) #
# d / dx (sin ^ -1 csc (4x)) = ((- 4 * csc 4x * barneseng 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 * barneseng 4x * sqrt (1-csc ^ 2 4x)) / (- cot ^ 2 4x)) #
# d / dx (sin ^ -1 csc (4x)) = 4 * sek 4x * sqrt (1-csc ^ 2 4x) #
Gud velsigne …. Jeg håber forklaringen er nyttig.
