Find the derivative of y = (x^2 + 1)(x^3 + 1) in two ways: by using the Product Rule and by performing the multiplicatino first. Do your answers agree?

Answer 1

I don't know if your answers agree. Can't you at least do the multiplication followed by differentiation?

For the product rule test, let u = x^2 +1 and v = x^3 +1.
Then d(uv)/dx = u dv/dx + v du/dx
= (x^2+1)*3x^2 + (x^3+1)*2x
= 3x^4 + 3x^2 + 2x^4 + 2x
= 5x^4 + 3x^2 + 2x

Now do it the other way and see of they agree