Question

1. Найдите первообразную у=cos5x-(2-6x)4
2. Найдите производную функций y=(x4-5х)(4x-5)

Answer 1

1)у=cos5x-(2-6x)⁴

F(x)=1/5*sin(5x)-1/5*(-1/6)*(2-6x)⁵+C=0,2*sin(5x)+1/30*(2-6x)⁵+C

2)y=(x⁴-5х)(4x-5)

y'=(x⁴-5х)' (4x-5)+(x⁴-5х)(4x-5)'=1)у=cos5x-(2-6x)⁴

F(x)=1/5*sin(5x)-1/5*(-1/6)*(2-6x)⁵+C=0,2*sin(5x)+1/30*(2-6x)⁵+C

2)y=(x⁴-5х)(4x-5)

y'=(x⁴-5х)' (4x-5)+(x⁴-5х)(4x-5)'=

=(4x³-5)(4x-5)+(x⁴-5х)*4=

=16x⁴-20x³-20x+25+4x⁴-20x=

=20x⁴-20x³-40x+25

=(4x³-5)(4x-5)+(x⁴-5х)*4=

=16x⁴-20x³-20x+25+4x⁴-20x=

=20x⁴-20x³-40x+25