a) [m]y`=2\cdot (x^{\frac{3}{4}})`=2\cdot (3/4)\cdot x^{\frac{3}{4}-1}=\frac{3}{2\sqrt[4]{x}}[/m]
б) [m]y`=-3\cdot (-5)x^{-5-1}+15\cdot 2x-2=\frac{15}{x^{6}}+30x-2[/m]
в)[m]y`=\frac{1}{cos^2(3x^4-5)x}\cdot ((3x^4-5)x)`+2\cdot (-\frac{1}{sin^2x})=\frac{1}{cos^2(3x^4-5)x}\cdot (3x^5-5x)`-\frac{2}{sin^2x}=\frac{15x^4-5}{cos^2(3x^4-5)x}-\frac{2}{sin^2x}[/m]
30.
∫ x^2(1+2x)dx= ∫ (x^2+2x^3)dx= ∫ x^2dx+2 ∫ x^3dx=[m]\frac{x^3}{3}+2\frac{x^4}{4}+C=\frac{x^3}{3}+\frac{x^4}{2}+C[/m]