Find the derivative of the following function: f(x) = x(x^3 + 2x)

f(x) becomes f'(x)1) First multiply out the brackets (by adding the indices) = x^4 + 2x^22) Then differentiate this. The indices moves to the front and multiplied by the number before the x. The indices is then decreased by 1.3) x^ 4 becomes 4x^34) 2x^2 becomes 4x^1... anything to the power of 1 is just itself so this becomes just 4x5) The final answer is f'(x) = 4x^3 + 4x