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

To begin with it is important to identify which method of differentiation is required here, since there are two terms multiplied together you would initially choose the product rule, differentiating (4x-3)^3 and sin2x separately. To differentiate the first term simply multiply the power by the coefficient of x which product is then multiplied by the bracket and the power reduces by 1. To differentiate sin2x, the trig rules must be remembered, which will give 2sin2x. To get the full differential multiply the second differential by the first term and then add the first differential by the second term.