Question

найдите производную функции 3x^6+x^4/4-2x^2+5x?

Answer 1

Ответ:

$y = \frac{3 {x}^{6} + {x}^{4} }{4 - 2 {x}^{2} + 5x }$

$y' = \frac{(3 {x}^{6} + {x}^{4} )'(4 - 2 {x}^{2} + 5x) - (4 - 2 {x}^{2} + 5x)'(3 {x}^{6} + {x}^{4} ) }{ {(4 - 2 {x}^{2} + 5x)}^{2} } = \\ = \frac{(18 {x}^{5} )(4 - 2 {x}^{2} + 5x) - ( - 4x + 5)(3 {x}^{6} + {x}^{4} ) }{ {(4 - 2 {x}^{2} + 5x)}^{2} } = \\ = \frac{72 {x}^{5} - 36 {x}^{7} + 90 {x}^{6} + 12 {x}^{7} + 4 {x}^{5} - 15 {x}^{6} - 5 {x}^{4} }{ {(4 - 2 {x}^{2} + 5x)}^{2} } = \\ = \frac{ - 24 {x}^{7} + 75 {x}^{6} + 76 {x}^{5} - 5 {x}^{4} }{ {4 - 2 {x}^{2} + 5x)}^{2} } = \\ = - \frac{ {x}^{4} (2 {x}^{3} - 75 {x}^{2} - 76x + 5) }{ {(4 - 2 {x}^{2} + 5x) }^{2} }$