Second derivative of $2 e^{x}$

The calculator will find the second derivative of $2 e^{x}$, with steps shown.

Related calculators: Derivative Calculator, Logarithmic Differentiation Calculator

Leave empty for autodetection.
Leave empty, if you don't need the derivative at a specific point.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

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

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

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 $c = 2$ and $f{\left(x \right)} = e^{x}$:

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

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

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

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

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

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 $c = 2$ and $f{\left(x \right)} = e^{x}$:

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

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

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

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

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

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