Question

Помогите найти производную!

Answer 1

Ответ:

1

$y' = ( {x}^{2} + x - 1)' \times tgx + (tgx)' \times ( {x}^{2} + x + 1) = \\ = (2x + 1) \times tgx + \frac{1}{ \cos {}^{2} (x) } \times ( {x}^{2} + x - 1) = \\ = (2x + 1)tgx + \frac{ {x}^{2} + x - 1}{ \cos {}^{2} (x) }$

2

$y' = ( log_{7}(x)) ' \times ( {x}^{3} + {3}^{x} ) + ( {x}^{3} + {3}^{ x} )' \times log_{7}(x) = \\ = \frac{1}{x ln(7) } \times ( {x}^{3} + {3}^{x} ) + (3 {x}^{2} + ln(3) \times {3}^{x} ) \times log_{7}(x)$

3

$y' = 4 \cos {}^{3} ( {x}^{2} + x ) \times ( \cos( {x}^{2} + x) )' \times ( {x}^{2} + x)' = \\ = 4 \cos {}^{3} ( {x}^{2} + x) \times ( - \sin( {x}^{2} + x)) \times (2x + 1) = \\ = - 4(2x + 1) \sin( {x}^{2} + x) \cos {}^{3} ( {x}^{2} + x ) = \\ = ( - 8x - 4) \sin( {x}^{2} + x ) \cos {}^{3} ( {x}^{2} + {?}^{2} )$

4

$y' = 5 log_{2} {}^{4} ( {x}^{2} + 3 ) \times ( log_{2}( {x}^{2} + 3)) ' \times ( {x}^{2} + 3)' = \\ = 5 log_{2} {}^{4} ( {x}^{2} + 3) \times \frac{1}{ ln(2) \times ( {x}^{2} + 3)} \times 2x = \\ = \frac{10 x log_{2} {}^{4} ( {x}^{2} + 3 ) }{ ln(2) \times ( {x}^{2} + 3) }$