1. Найдите производную функции а)f(x)=x^3-10x^2+5x+1 б)f(x)=2/x^7+4 корня из...

$f'(x)=(x^3-10x^2+5x+1)'=(x^3)-(10x^2)'+(5x)'+(1)'=3x^{3-1}-10(x^2)'+5(x)'+0=3x^2-10*2x^{2-1}+5*1=3x^2-20x+5$

$f'(x)=(\frac{2}{x^7} +4\sqrt{3})'=(2x^{-7})'+(4\sqrt{3})'=2(x^{-7})'+0=2*(-7)x^{-7-1}=-14x^{-8}=-\frac{14}{x^8}$

$\frac{2}{x^4+4\sqrt{3}}'=-\frac{2}{(x^4+4\sqrt{3})^2}*(x^4+\sqrt{3})'=\frac{-2}{(x^4+4\sqrt{3})^2}*4x^3=\frac{-8x^3}{(x^4+4\sqrt{3})^2}$

$f'(x)=((5x^2+2)\sqrt{x})'=(5x^2+2)'*(\sqrt{x})+(5x^2+2)*(\sqrt{x})'=(5*2x+0)*(\sqrt{x})+(5x^2+2)*\frac{1}{2\sqrt{x}}=10x\sqrt{x}+\frac{5x^2+2}{2\sqrt{x}}=\frac{10x^2+5x^2+2}{2\sqrt{x}}=\frac{15x^2+2}{2\sqrt{x}}$