Differentiate y=x^3*(x^2+1)

As this is a product of two functions it is necessary to use the product rule for differentiation. Therefore one of the functions must labeled v and the other u. i.e. u=x^3 and v=(x^2+1). It is then necessary to differentiate each of those functions seperately so that du/dx=3x^2 and dv/dx=2x. The final step is to multiply v by du/dx and multiply v by du/dx then add the two together as follows: dy/dx=2x^4+3x^2*(x^2+1)