12.07.2015 Views

RIJEÅ ENI ZADACI IZ MATEMATIKE

RIJEÅ ENI ZADACI IZ MATEMATIKE

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10. Nadite prvu derivaciju funkcije f(x) = (1 + x 2 ) 100 .Rješenje:f ′ (x) = [(1 + x 2 ) 100 ] ′f ′ (x) = 100(1 + x 2 ) 99 (1 + x 2 ) ′f ′ (x) = 100(1 + x 2 ) 99 · 2xf ′ (x) = 200x(1 + x 2 ) 9911. Nadi prvu derivaciju funkcije f(x) = √ 1 − 3x 4 .Rješenje:f ′ 1(x) =2 √ 1 − 3x · (1 − 4 3x4 ) ′f ′ 1(x) =2 √ 1 − 3x · 4 (−12x3 )f ′ (x) =−6x3 √1 − 3x410

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