1)
у=3х³+4х²-5х^6+1
3x²
y/(x)=(3x³+4x²-5x^6+1)/×3x²-(3x³+4x²-5x^6+1)×(3x²)/=
(3x²)²
=(9x²+8x-30x^5)×3x²-(3x³+4x²-5x^6+1)×6x
9x^4
=27x^4+24x³-90x^7-18x^4-24x³+30x^7-6x=
9x^4
=-60x^7+9x^4-6x= 3x(-20x^6+3x³-2) = -20x^6+3x³-2
9x^4 9x^4 x³
2)
y=(5x-7)(2x+10)
y/(x)=(5x-7)/(2x+10)+(5x-7)(2x+10)/=5(2x+10)+(5x-7)×2=10x+50+10x-14=
=20x+36
3)
y=(2x³+5x²-1)(5x^4+2x²)
y/(x)=(2x³+5x²-1)/(5x^4+2x²)+(2x³+5x²-1)(5x^4+2x²)/=
=(6x²+10x)(5x^4+2x²)+(2x³+5x²-1)(20x³+4x)=
=30x^6+12x^4+50x^5+20x³+40x^6+8x^4+100x^5+20x³-20x³-4x=
=70x^6+150x^5+20x^4+20x³-4x
4)
y=5x²
x+10
y/(x)=(5x²)/×(x+10)-(x+10)/×5x²
(x+10)²
y/(x)=10x(x+10)-5x² y/(x)= 10x²+100x-5x² y/(x)=5x²+100x
(x+10)² (x+10)² (x+10)²