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Given that y=sin2x(3x-1)^4, find dy/dx

This is an example of the product rule. In this, y=uv and dy/dx = u(dv/dx) + v(du/dx) u = sin2x so du/dx = 2 * cos2x = 2cos2x v = (3x-1)4 so dv/dx = 4 * 3 * (3x-1)3 = 12(3x-1)3 Therefore dy/dx = sin2x * 12(3x-1)3 + (3x-1)4 * 2cos2x = 12sin2x(3x-1)3 + 2cos2x(3x-1)4

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