Предмет: Алгебра, автор: leronburova2006

ПОМОГИТЕ ОЧЕНЬ ПРОШУ 67 БАЛОВ
Обчисліть значення похідної функції f у точці x0
f(x)=In(2x+1) X0=1,5

Знайдіть похідну функції
y=In^2(5x+1)

Приложения:

Simba2017: f`(x)=2/(2x+1); f`(1.5)=2/4=1/2

Simba2017: y`=2ln(5x+1)*5/(5x+1)=10ln(2x+1)/(5x+1)

Ответы

Автор ответа: nepustilipoeta

производная функции f(x)=In(2x+1) равна 2/(2х+1), в точке 1.5, соответственно 2/(2*1.5+1)=2/4=0.5

производная функции y=In²(5x+1) равна (2*5In(5x+1))/(5х+1)=(10In(5x+1))/(5х+1)

находили как производную сложной функции, в первом задании производная от логарифма умножалась на производную линейной функции, во втором задании производная степенной функции умножалась на производную логарифмической и линейной.

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