Question

Найдите производные функций

Answer 1

Ответ:

1

$y' = 20 {x}^{4} - 8 {x}^{2} + 0 = 20 {x}^{4} - 8 {x}^{2}$

2

$y' = ( {x}^{6} - 3 {x}^{ - 2} + {x}^{ \frac{1}{2} } - 6 {x}^{ \frac{2}{3} } )' = \\ = 6 {x}^{5} + 6 {x}^{ - 3} + \frac{1}{2} {x}^{ - \frac{1}{2} } - 6 \times \frac{2}{3} {x}^{ - \frac{1}{3} } = \\ = 6 {x}^{5} + \frac{6}{ {x}^{3} } + \frac{1}{2 \sqrt{x} } - \frac{4}{ \sqrt[3]{x} }$

3

$y' = \frac{(x) '\sin(x) + ( \sin(x))' \times x }{ \sin {}^{2} (x) } = \\ = \frac{ \sin(x) - x \cos(x) }{ \sin {}^{2} (x) }$

4

$y' = \frac{1}{x} + {e}^{x} + x {e}^{x}$

5

$y = ( {x}^{3} + {3}^{x} )' \times tgx + (tgx) '\times ( {x}^{3} + {3}^{ x} ) = \\ = (3 {x}^{2} + {3}^{x} \times ln(3) )tgx + \frac{ {x}^{3} + {3}^{x} }{ \cos {}^{2} (x) }$