Ako rozlišujete f (x) = tan (e ^ ((lnx-2) ^ 2) pomocou pravidla reťazca.?

odpoveď:

# ((2sec ^ 2 (e ^ ((ln (x) -2) ^ 2) e ^ ((ln (x) -2) ^ 2) (lnx-2)) / x) #

vysvetlenie:

# d / dx (tan (e ^ ((ln (x) -2) ^ 2)) = sec ^ 2 (e ^ ((ln (x) -2) ^ 2) * d / dx ((e ^ ((ln (x) -2) ^ 2)) #

=# sec ^ 2 (e ^ ((ln (x) -2) ^ 2) e ^ ((((ln (x) -2)) 2) * d / dx (ln (x) -2) ^ 2 #

=# sec ^ 2 (e ^ ((ln (x) -2) ^ 2) e ^ (((ln (x) -2)) 2) 2 (lnx-2) * d / dx (lnx-2)) #

=# (sek ^ 2 (e ^ ((ln (x) -2) ^ 2) e ^ (((ln (x) -2)) 2) 2 (lnx-2) * 1 / x) #

=# ((2sec ^ 2 (e ^ ((ln (x) -2) ^ 2) e ^ ((ln (x) -2) ^ 2) (lnx-2)) / x) #