how can differentiate using the product and chain rule? e.g y=(4x+1)^3(sin2x), find dy/dx.

First you have to identify the equation for y is a product. Then you can apply the product rule using (4x+1)^3 as one term and sin2x as the other. First you differentiate (4x+1)^3 using the chain rule. You do this by multiplying the expression by the exponent which is 3 then differentiate what is inside the bracket and multiply by this then you decrease the exponent by one. Once this first term is differentiated you multiply by the second term sin2x. Then you add the first term (4x+1)^3 multiplied by the derivative of sin(2x), which again uses the chain rule.