Question

Найдите производную
1. f(x)=(2-x)(x+3)
2.f(x)=(2x+1)(x-√x)

Answer 1

1.

$f'(x) = (2 - x)'(x + 3) + (x + 3)'(2 - x) = \\ = - (x + 3) + (2 - x) = - x - 3 + 2 - x = - 2x - 1$

2.

$f'(x) = (2x + 1)'(x - \sqrt{x} ) + (x - \sqrt{x} )'(2x + 1) = \\ = 2(x - \sqrt{x} ) + (1 - \frac{1}{2} {x}^{- \frac{1}{2} } )(2x + 1) = \\ = 2x - 2 \sqrt{x} + (1 - \frac{1}{2 \sqrt{x} } )(2x + 1) = \\ = 2x - 2 \sqrt{x} + 2x + 1 - \sqrt{x} - \frac{1}{2 \sqrt{x} } = \\ = 4x - 3 \sqrt{x} + 1 - \frac{1}{2 \sqrt{x} }$