Question

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Answer 1

$\displaystyle\bf\\1)\\\\y=x^{2} (5-x^{3})\\\\y'=(x^{2} )'\cdot(5-x^{3})+x^{2} \cdot(5-x^{3} )'=2x\cdot(5-x^{3} )+x^{2} \cdot(-3x^{2})=\\\\=10x-2x^{4}-3x^{4} =10x-5x^{4} \\\\2)\\\\y=-7x(x^{2} -4)\\\\y'=(-7x)'\cdot(x^{2} -4)+(-7x)\cdot(x^{2} -4)'=\\\\=-7\cdot(x^{2} -4)-7x\cdot 2x=-7x^{2} +28-14x^{2} =28-21x^{2} \\\\3)\\\\y=5(x+3)^{2} \\\\y'=5'\cdot(x+3)^{2} +5\cdot[(x+3)^{2} ]'=0+5\cdot2(x+3)=10x+30\\\\4)\\\\y=(x-3)(x^{2} -2x+4)$

$\displaystyle\bf\\y'=(x-3)'\cdot(x^{2} -2x+4)+(x-3)\cdot(x^{2} -2x+4)'=\\\\=1\cdot(x^{2} -2x+4)+(x-3)\cdot(2x-2)=\\\\=x^{2} -2x+4+2x^{2} -2x-6x+6=3x^{2} -10x+10$