Question

Найдите производную функцию : 1. y=(x^2-1)(x^4+2) 2.y=(x^3+1)sqrt x 3.y=x^3/2x+4 4.y=x^2/x^2-1

Answer 1

1.
$y=(x^2-1)(x^4+2) = x^6 - x^4 + 2x^2 - 2\\ y' = 6x^5-4x^3+4x$

2.
$y=(x^3+1) \cdot \sqrt{x}\\ y' = (x^3+1)' \cdot \sqrt{x} + (x^3+1) \cdot (\sqrt{x})' = 3x^2\sqrt{x} + \frac{x^3+1}{2\sqrt{x}}$

3.
$y=\frac{x^3}{2x+4}\\ y'=\frac{(x^3)' \cdot (2x+4) - x^3 \cdot (2x+4)'}{(2x+4)^2} = \frac{- x^3+12x^2}{4x^2+16x+16}$

4.

$y=\frac{x^2}{x^2 - 1}\\ y' = \frac{2x(x^2 - 1) - 2x \cdot x^2}{(x^2 - 1)^2}$