Find the derivative of the function y=3x^2e^(2x)sin(x).

y is the product of three different function, so we would use the product rule in order to calculate the derivative of the curve. In order to apply the product rule we need to find the derivatives of each of the three functions separately. y₁=3x²         -->      dy₁/dx = 6x [by simply using the chain rule of differentiation] y₂=e^2x         -->      dy₂/dy = 2e^2x y₃=sin(x)     -->      dy₃/dx = cos(x) According to the product rule each function is to be differentiated one at a time and the other functions remain unchanged. Therefore the derivative of the function y=3x²e^2xsin(x) is: dy/dx = 6xe^2xsin(x) + 6x²e^2xsin(x) + 3x²e^2xcos(x).