What is the derivative of x3 + 2x?

The derivative of $x^3 + 2x$ is $3x^2 + 2$.

Steps: To find the derivative, we apply the sum rule and the power rule for differentiation:

1. Derivative of $x^3$: Using the power rule $\frac{d}{dx}(x^n) = nx^{n-1}$, we get $\frac{d}{dx}(x^3) = 3x^{3-1} = 3x^2$.
2. Derivative of $2x$: Using the constant multiple rule and the power rule, we get $\frac{d}{dx}(2x) = 2 \cdot \frac{d}{dx}(x^1) = 2 \cdot 1x^{1-1} = 2 \cdot 1x^0 = 2 \cdot 1 = 2$.
3. Sum the derivatives: $\frac{d}{dx}(x^3 + 2x) = \frac{d}{dx}(x^3) + \frac{d}{dx}(2x) = 3x^2 + 2$.