3. (u*v)'=u'v+uv'

а) y'(x)=3x²(x²-3)+(x³+4)*2x=3x⁴-9x²+2x⁴+8x=5x⁴-9x²+8x;

б) (u/v)'=(u'v-uv')/v²

y'(x)=(6(4-3x)-(6x+5)*(-3))/(4-3x)²=(24-18x+18x+15)/(4-3x)²=39/(4-3x)²

Ответ:

1) Производная произведения   [tex](uv)'=u'v+uv'[/tex]  .

[tex]y=(x^3+4)(x^2-3)\\\\y'=3x^2(x^2-3)+(x^3+4)\cdot 2x=3x^4-9x^2+2x^4+8x=5x^4-9x^2+8x[/tex]

2) Производная дроби    [tex]\Big(\dfrac{u}{v}\Big)'=\dfrac{u'v-uv'}{v^2}[/tex]   .

[tex]y=\dfrac{6x+5}{4-3x}\\\\y'=\dfrac{6\, (4-3x)-(6x+5)\cdot (-3)}{(4-3x)^2}=\dfrac{24-18x+18x+15}{(4-3x)^2}=\dfrac{39}{(4-3x)^2}[/tex]