Calculus Examples

$g (x) = e^{x} (\tan (x - x))$

Step 1

Differentiate using the Constant Multiple Rule.

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Step 1.1

Subtract $x$ from $x$ .

$\frac{d}{d x} [e^{x} \tan (0)]$

Step 1.2

Since $\tan (0)$ is constant with respect to $x$ , the derivative of $e^{x} \tan (0)$ with respect to $x$ is $\tan (0) \frac{d}{d x} [e^{x}]$ .

$\tan (0) \frac{d}{d x} [e^{x}]$

Step 2

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

$\tan (0) e^{x}$

Step 3

Simplify.

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Step 3.1

Reorder the factors of $\tan (0) e^{x}$ .

$e^{x} \tan (0)$

Step 3.2

The exact value of $\tan (0)$ is $0$ .

$e^{x} \cdot 0$

Step 3.3

Multiply $e^{x}$ by $0$ .

$0$