RIJEÃ…Â ENI ZADACI IZ MATEMATIKE

√ 1−x14. Nadi prvu derivaciju funkcije f(x) = e x+1 .Rješenje:√f ′ 1−x(x) = e x+1 ·√√f ′ 1−x(x) = e x+11 − x · (x + 1 )′√f ′ 1−x(x) = e x+1 ·1√21−xx+1f ′ (x) = ef ′ (x) =f ′ (x) =1√21−xx+1· ( 1 − xx + 1 )′· (1 − x)′ · (x + 1) − (1 − x) · (x + 1) ′(x + 1) 2√ 1−xx+1 ·1√2−e√1−xx+11−xx+1·√ 1−xx+1· (x + 1)2√ 1−x−2(x + 1) 2−e x+1√ 31 − x · (x + 1) 2f ′ (x) =√ 1−x−e x+1√ √1 − x · (x + 1)3f ′ (x) =√ 1−x−e x+1√ √ 1 − x · (x + 1) · x + 1f ′ (x) =f ′ (x) =−e√ 1−xx+1(x + 1) · √(1− x)(x + 1)−e√ 1−xx+1(x + 1) · √1− x 212