Español | Português
  1. Home
  2. Calculators
  3. Calculators: Calculus I
  4. Calculus Calculator

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

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.

Your Input

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

Solution

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

Answer

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