# Second derivative of $$$x^{3}$$$

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### Your Input

**Find $$$\frac{d^{2}}{dx^{2}} \left(x^{3}\right)$$$.**

### Solution

**Find the first derivative $$$\frac{d}{dx} \left(x^{3}\right)$$$**

**Apply the power rule $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ with $$$n = 3$$$:**

Thus, $$$\frac{d}{dx} \left(x^{3}\right) = 3 x^{2}$$$.

**Next, $$$\frac{d^{2}}{dx^{2}} \left(x^{3}\right) = \frac{d}{dx} \left(3 x^{2}\right)$$$**

**Apply the constant multiple rule $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$ with $$$c = 3$$$ and $$$f{\left(x \right)} = x^{2}$$$:**

**Apply the power rule $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ with $$$n = 2$$$:**

Thus, $$$\frac{d}{dx} \left(3 x^{2}\right) = 6 x$$$.

Therefore, $$$\frac{d^{2}}{dx^{2}} \left(x^{3}\right) = 6 x$$$.

### Answer

**$$$\frac{d^{2}}{dx^{2}} \left(x^{3}\right) = 6 x$$$A**