Задача 77147 ...

662ea278a297581bd840b37f

4/28/2024 7:25:20 PM

Вычислите значение производной функции f(x) = (2x-3)/sin x в точке x = π/4.

5f3eaa23faf909182968dde0

4/29/2024 1:49:49 PM

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№ 4
f(x)=(2x-3)/sinx,
f'(x)=((2x-3)'*sinx-(2x-3)*(sinx)')/(sin^(2)x)=(2sinx-(2x-3)cosx)/(sin^(2)x),
f'(π/4)=(2sin(π/4)-(2*(π/4)-3)*cos(π/4))/(sin^(2)(π/4))=
=(2*(sqrt(2)/2)-((π/2)-3)*(sqrt(2)/2))/(sqrt(2)/2)^(2))=
=(sqrt(2)-((π/2)-3)*(sqrt(2)/2))/(1/2)=2sqrt(2)-((π/2-3)sqrt(2))=
=sqrt(2)*(2-(π/2)+3)=(5-(π/2))sqrt(2).