Derivative & Integral

Step-by-step solution

1. 1

   Differentiate the polynomial

   Apply the power rule d/dx [a·x^n] = n·a·x^(n-1) to x^3 + 2x + 3.

   $$\frac{d}{dx}\left[x^{3} + 2x + 3\right]$$
2. 2

   Derivative of the constant term

   d/dx [3] = 0 (constant drops out)

   $$\frac{d}{dx}\left[3\right] = 0$$
3. 3

   Apply the power rule to the degree-1 term

   $$\frac{d}{dx}\left[2x\right] = 1 \cdot 2 = 2$$

   • d/dx [2·x] = 1·2·x^0 = 2
4. 4

   Apply the power rule to the degree-3 term

   $$\frac{d}{dx}\left[x^{3}\right] = 3 \cdot x^{2} = 3x^{2}$$

   • d/dx [1·x^3] = 3·1·x^2 = 3·x^2
5. 5

   Result

   d/dx [x^3 + 2x + 3] = 3x^2 + 2

   $$f'(x) = 3x^{2} + 2$$