Предмет: Алгебра, автор: ilnarsuper

Вычислите производные функций,
Помогите решить 1 задание.

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Автор ответа: SYSTEMCORE

0

$displaystyle a)quad y'=(3x^4+5x^3-2x^2+10x)'=3cdot4x^3+5cdot3x^2-2cdot2x+10=\\=boxed{12x^3+15x^2-4x+10}\\\b)quad y'=(2x^3(3x+4))'=(6x^4+8x^3)'=24x^3+24x^2=boxed{24x^2(x+1)}\\\c)quad y'=bigg(frac{5x^4+1}{x^2}bigg)'=frac{(5x^4+1)'cdot x^2-(x^2)'(5x^4+1)}{x^4}=\\\=frac{20x^3cdot x^2-2x(5x^4+1)}{x^4}=frac{20x^4-10x^4-2}{x^3}=boxed{frac{10x^4-2}{x^3}}\\\d)quad y'=((3x^2+4x)^{83})'=83(3x^2+4x)^{82}cdot(3x^2+4x)'=\\=boxed{83(3x^2+4x)^{82}cdot(6x+4)}$

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