1) y' = 2(x^6/6 -5/∛x^10 +4x) * (x^6/6 -5/∛x^10 +4x)' =
=2(x^6/6 -5/∛x^10 +4x) * (x^5 +50/3*x^-13/3 +4)
2)y'= 7^1/x * ln7 *(1/x)' = - 7^1/x * ln7 * 1/x²
3) y'=1/((1+3x)/(1 +9x²)) * ((1+3x)/(1 +9x²)) ' =
= 1/((1+3x)/(1 +9x²)) * ( 3(1+9x²) - (1+3x)*18x) )/(1 +9x²)²=
= 1/((1+3x)/(1 +9x²)) * (3+27x² -18x-54x²)/(1 +9x²)²=
= 1/((1+3x)/(1 +9x²)) * (3 -27x² -18x)/(1 +9x²)
4)y' =(-1/√(1 - x²) *√(1 - x²) - arcCosx * 1/2√(1 - x²) * (- 2x) )/(1 - x²)
5)y' = 21^Sin(4x) *ln21 * Cos(4x) * 4
6)y = Sin⁻³(1 +2x)
y' = -3Sin⁻⁴(1 +2x ) * Cos(1 +2x) * 2=
=-6Cos(1 +2x)/Sin⁴(1 +2x)