Calculus Examples

$f (x) = 69 + 102 e^{- 0.033 \cdot 4}$

Step 1

Multiply $- 0.033$ by $4$ .

$\frac{d}{d x} [69 + 102 e^{- 0.132}]$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{d}{d x} [69 + 102 \frac{1}{e^{0.132}}]$

Step 3

Differentiate.

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Step 3.1

By the Sum Rule, the derivative of $69 + 102 \frac{1}{e^{0.132}}$ with respect to $x$ is $\frac{d}{d x} [69] + \frac{d}{d x} [102 \frac{1}{e^{0.132}}]$ .

$\frac{d}{d x} [69] + \frac{d}{d x} [102 \frac{1}{e^{0.132}}]$

Step 3.2

Since $69$ is constant with respect to $x$ , the derivative of $69$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [102 \frac{1}{e^{0.132}}]$

Step 4

Evaluate $\frac{d}{d x} [102 \frac{1}{e^{0.132}}]$ .

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Step 4.1

Combine $102$ and $\frac{1}{e^{0.132}}$ .

$0 + \frac{d}{d x} [\frac{102}{e^{0.132}}]$

Step 4.2

Since $\frac{102}{e^{0.132}}$ is constant with respect to $x$ , the derivative of $\frac{102}{e^{0.132}}$ with respect to $x$ is $0$ .

$0 + 0$

Step 5

Add $0$ and $0$ .

$0$