Задача 79481 Решите по теме: Производные 1) [m] y =...

65340659cb334f3437d1546b

2/28/2025 6:31:19 AM

Решите по теме: Производные

1) [m] y = 3x^4 - x^3 - 7 [/m]

2) [m] y = 2\sin 2x - \cot x [/m]

3) [m] y = (x^2 - 3)\sqrt{x} [/m]

4) [m] y = \frac{2x^2}{x^3 - 1} [/m]

5) [m] y = \sin \left( 3x - \frac{\pi}{4} \right), \, x_0 = \frac{\pi}{4} [/m]

6) [m] y = \sqrt{7x - 3}, \, x_0 = 1 [/m]

7) [m] y = (x^3 - 2x^2 + 3)^{17} [/m]

5f3eaa23faf909182968dde0

2/28/2025 7:05:32 AM

★

1) y'=12x^(3)-3x^(2)
2) y'=4cos2x+(1/sin^(2)x)
3) y'=(x^(2)-3)'*sqrt(x)+(x^(2)-3)*(sqrt(x))'=2xsqrt(x)+((x^(2)-3)/(2sqrt(x)))
4) y'=[m]\frac{(2x^2)'*(x^3-1)-2x^2*(x^3-1)'}{(x^3-1)^2}=\frac{4x(x^3-1)-2x^2*3x^2}{(x^3-1)^2}=\frac{4x^4-4-6x^4}{(x^3-1)^2}=-\frac{2x^2+4}{(x^3-1)^2}.[/m]
5) y'=3cos(3x-(π/4)),
y'(π/4)=3cos((3π/4)-(π/4))=3cos(π/2)=3*0=0
6) y'=7/(2sqrt(7x-3)),
y'(1)=7/(2sqrt(7*1-3))=7/(2*2)=7/4
7) y'=17(x^(3)-2x^(2)+3)^(16)*(3x^(2)-4x)