75²/45³=3²·5⁴/(3⁶·5³)= (сократим на 3²и 5³) = (3²⁻²·5⁴⁻³)/(3⁶⁻²·5³⁻³)=5/3⁴=5/81
Подробно
(75)² =(3·5·5)²=3²·5²·5²=3²·5⁴
(45)³=(3·3·5)³=3³·3³·5³=3⁶·5³
y=5√x-4x^3/6
y=(x^3-3)*(3x^5+x)
y`=( x^3-3)’*(3x^5+x) + (x^3-3)*(3x^5+x)’ =3x^2*(3x^5+x)+
(x^3-3)(15x^4+1)=9x^7+3x^3+15x^7-45x^4+4x^3-3
y=6sin x -ctg x
y`=6cosx+1/sin2x
y=cos x * x5
y`=(cosx)’*x5+cosx*(x5)’=-sinx*x5+5x^4cosx
Sin²(π-π/3)cos(π-π/4)ctg²π/4=sin²π/3*(-cosπ/4)*ctg²π/4=3/4*(-√2/2)*1=-3√2/8