found using calculus, specifically the power rule for differentiation. The power rule states that the derivative of x^n with respect to x is n*x^(n-1).
Firstly, we look at the term 2x. This can be considered as x to the power of 1, multiplied by 2. According to the power rule, the derivative of x^1 is 1*x^(1-1) = 1. Therefore, after applying the power rule to this term, 2*1 = 2 (since the constant multiplies).
Next, we look at the term x^3. Applying the power rule, the derivative of x^3 is 3*x^(3-1)=3x^2.
Finally, we add together the derivatives of both terms to get the derivative of the whole function. The derivative f'(x) is therefore 3x^2 + 2.