Calculus Examples

$f (x) = 10 e^{x}$

Step 1

Find the first derivative.

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Step 1.1

Since $10$ is constant with respect to $x$ , the derivative of $10 e^{x}$ with respect to $x$ is $10 \frac{d}{d x} [e^{x}]$ .

$10 \frac{d}{d x} [e^{x}]$

Step 1.2

Differentiate using the Exponential Rule which states that $\frac{d}{d x} [a^{x}]$ is $a^{x} \ln (a)$ where $a$ = $e$ .

$f' (x) = 10 e^{x}$

Step 2

Find the second derivative.

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Step 2.1

Since $10$ is constant with respect to $x$ , the derivative of $10 e^{x}$ with respect to $x$ is $10 \frac{d}{d x} [e^{x}]$ .

$10 \frac{d}{d x} [e^{x}]$

Step 2.2

Differentiate using the Exponential Rule which states that $\frac{d}{d x} [a^{x}]$ is $a^{x} \ln (a)$ where $a$ = $e$ .

$f'' (x) = 10 e^{x}$

Step 3

The second derivative of $f (x)$ with respect to $x$ is $10 e^{x}$ .

$10 e^{x}$