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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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Your Input

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

Solution

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

Answer

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