Statement Compute the derivative of y=x2 e4xy=x^{2}\,e^{4x}y=x2e4x. Solution Product rule: y′=2x e4x+x2⋅4e4xy'=2x\,e^{4x}+x^{2}\cdot 4e^{4x}y′=2xe4x+x2⋅4e4x. y′=e4x (4x2+2x)=2x e4x(2x+1).y'=e^{4x}\,(4x^{2}+2x)=2x\,e^{4x}(2x+1).y′=e4x(4x2+2x)=2xe4x(2x+1).