Using the product rule, differentiate y=(2x)(e^3x)
The product rule states that if y=uv, where u and v are both functions of x, then dy/dx = u(dv/dx) + v(du/dx)Therefore, the differential of 2xe3x can be found by letting 2x=u and e3x =v.u=2x,du/dx = 2
v=e3xdv/dx = 3e3x
dy/dx = u(dv/dx) + v(du/dx)dy/dx = 2x(3e3x) + e3x(2)dy/dx = 6xe3x + 2e3xdy/dx = 2e3x(3x+1)
