# Second derivative of $x$

The calculator will find the second derivative of $x$, with steps shown.

Related calculators: Derivative Calculator, Logarithmic Differentiation Calculator

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

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

Apply the power rule $\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$ with $n = 1$, in other words, $\frac{d}{dx} \left(x\right) = 1$:

$${\color{red}\left(\frac{d}{dx} \left(x\right)\right)} = {\color{red}\left(1\right)}$$

Thus, $\frac{d}{dx} \left(x\right) = 1$.

### Next, $\frac{d^{2}}{dx^{2}} \left(x\right) = \frac{d}{dx} \left(1\right)$

The derivative of a constant is $0$:

$${\color{red}\left(\frac{d}{dx} \left(1\right)\right)} = {\color{red}\left(0\right)}$$

Thus, $\frac{d}{dx} \left(1\right) = 0$.

Therefore, $\frac{d^{2}}{dx^{2}} \left(x\right) = 0$.

$\frac{d^{2}}{dx^{2}} \left(x\right) = 0$A