Упр.202 ГДЗ Колягин Ткачёва 11 класс (Алгебра)

2) (5x-4)6;
3) (1-3x)7;
4) 4/(3x-1)2;
5) 1/(2-3x)4;
6) 1/(4-3x)5.

1. $$y=(3x+1)^5$$
   $$y’ = 5(3x+1)^4 \cdot 3 = 15(3x+1)^4$$
2. $$y=(5x-4)^6$$
   $$y’ = 6(5x-4)^5 \cdot 5 = 30(5x-4)^5$$
3. $$y=(1-3x)^7$$
   $$y’ = 7(1-3x)^6 \cdot (-3) = -21(1-3x)^6$$
4. $$y=\frac{4}{(3x-1)^2}=4(3x-1)^{-2}$$
   $$y’ = 4\cdot (-2)(3x-1)^{-3}\cdot 3 = -24(3x-1)^{-3} = -\frac{24}{(3x-1)^3}$$
5. $$y=\frac{1}{(2-3x)^4}=(2-3x)^{-4}$$
   $$y’ = -4(2-3x)^{-5}\cdot (-3)=12(2-3x)^{-5}=\frac{12}{(2-3x)^5}$$
6. $$y=\frac{1}{(4-3x)^5}=(4-3x)^{-5}$$
   $$y’ = -5(4-3x)^{-6}\cdot (-3)=15(4-3x)^{-6}=\frac{15}{(4-3x)^6}$$

Ответ

1) $$y’=15(3x+1)^4$$;
2) $$y’=30(5x-4)^5$$;
3) $$y’=-21(1-3x)^6$$;
4) $$y’=-\frac{24}{(3x-1)^3}$$;
5) $$y’=\frac{12}{(2-3x)^5}$$;
6) $$y’=\frac{15}{(4-3x)^6}$$.