Question

Найти производную функций

Answer 1

1)

$y = \arctg( \sqrt{x - 4} ) \\ y' = ( \sqrt{x - 4})'( \arctg(g))' = \frac{1}{2 \sqrt{x - 4} } \times \frac{1}{1 + {g}^{2} } = \\ = \frac{1}{2(1 + {( \sqrt{x - 4} })^{2} ) \sqrt{x - 4} } = \frac{1}{2 \sqrt{x - 4}(x - 3) }$

2)

$y = \arcsin( {x}^{2} - 5x) + \tan(2x + 1) \\ y' = ( {x}^{2} - 5x)'( \arcsin(g))' + (2x + 1)'( \tan(h) )' = \\ = \frac{2x - 5}{ \sqrt{1 - {x}^{2} } } + \frac{2}{ \cos^{2} (x) }$