Question

Пожалуйста, помогите Найти производную

Answer 1

1.

$(5 {x}^{4} \times {e}^{ - 4x} ) '= (5 {x}^{4} )' \times {e}^{ - 4x} + ( {e}^{ - 4x} )' \times 5 {x}^{4} = \\ = 20 {x}^{3} \times {e}^{ - 4x} - 4 {e}^{ - 4x} \times 5 {x}^{4} = \\ = {e}^{ - 4x} (20 {x}^{3} - 20 {x}^{4} ) = \\ = 20 {x}^{3} {e}^{ - 4x} (1 - x)$

2.

$(9 {x}^{4} \times {e}^{ - 4x} ) '= (9 {x}^{4} )' \times {e}^{ - 4x} + ( {e}^{ - 4x} )' \times 9 {x}^{4} = \\ = 36 {x}^{3} {e}^{ - 4x} - 4 {e}^{ - 4x} \times 9 {x}^{4} = \\ = {e}^{ - 4x} (36 {x}^{3} - 36 {x}^{4} ) = \\ = 36 {x}^{3} {e}^{ - 4x} (1 - x)$