Найти производную функции 1.) y=8x-1/x^2+3 2.) y=(2x+x^3) (4-x^2)

1) [latex]y'= (\frac{8x-1}{x^2+3})'= \frac{(8x-1)'(x^2+3)-(8x-1)(x^2+3)'}{(x^2+3)^2}= \frac{8(x^2+3)-(8x-1)2x}{(x^2+3)^2}= [/latex] [latex]= \frac{8x^2+24-16x^2+2x}{(x^2+3)^2}= \frac{-8x^2+2x+24}{(x^2+3)^2} [/latex] 2) [latex]y'=((2x+x^3)(4-x^2))'=(2x+x^3)'(4-x^2)+(2x+x^3)(4-x^2)'=[/latex] [latex]=(x+3x^2)(4-x^2)+(2x+x^3)(-2x)=[/latex] [latex]=4x-x^3+12x^2-3x^4-4x^2-2x^4=-5x^4-x^3+8x^2[/latex]