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)
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