Second derivative of $e^{x}$

The calculator will find the second derivative of $e^{x}$, with steps shown.

Related calculators: Derivative Calculator, Logarithmic Differentiation Calculator

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

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

The derivative of the exponential is $\frac{d}{dx} \left(e^{x}\right) = e^{x}$:

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

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

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

The derivative of the exponential is $\frac{d}{dx} \left(e^{x}\right) = e^{x}$:

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

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

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

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