Given y=2x(x^2-1)^5, show that dy/dx = g(x)(x^2-1)^4 where g(x) is a function to be determined.

y=2x(x²-1)⁵ --> y=uv, where u=2x; v=(x²-1)⁵ --> thus product rule required.u'=2v'=10x(x²-1)⁴Product rule: dy/dx = uv' + v'uTherefore: dy/dx = 2x(10x(x²-1)⁴) + 2(x²-1)⁵ g(x) = (22x²-2)