Derivative of (5x-4)⁵(4-x³)⁵. Let u=5x-4 and v=4-x³, so du/dx=5 and dv/dx=-3x².
Let w=(uv)⁵=(5x-4)⁵(4-x³)⁵,
so dw/dx=5(uv)⁴(d(uv)/dx)=5(uv)⁴(vdu/dx+udv/dx)=
5(5x-4)⁴(4-x³)⁴(5(4-x³)-3x²(5x-4))=5(5x-4)⁴(4-x³)⁴(20-5x³-15x³+12x²)=
5(5x-4)⁴(4-x³)⁴(20+12x²-20x³)=20(5x-4)⁴(4-x³)⁴(5+3x²-5x³).