Question

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

Answer 1

1)
$y'= (frac{8x-1}{x^2+3})'= frac{(8x-1)'(x^2+3)-(8x-1)(x^2+3)'}{(x^2+3)^2}= frac{8(x^2+3)-(8x-1)2x}{(x^2+3)^2}=$
$= frac{8x^2+24-16x^2+2x}{(x^2+3)^2}= frac{-8x^2+2x+24}{(x^2+3)^2}$

2)
$y'=((2x+x^3)(4-x^2))'=(2x+x^3)'(4-x^2)+(2x+x^3)(4-x^2)'=$
$=(x+3x^2)(4-x^2)+(2x+x^3)(-2x)=$
$=4x-x^3+12x^2-3x^4-4x^2-2x^4=-5x^4-x^3+8x^2$