Calculus Examples

$g (t) = \frac{27500}{1 + 10 e^{- 2.72}}$

Step 1

Simplify the denominator.

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Step 1.1

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

$\frac{d}{d x} [\frac{27500}{1 + 10 \frac{1}{e^{2.72}}}]$

Step 1.2

Combine $10$ and $\frac{1}{e^{2.72}}$ .

$\frac{d}{d x} [\frac{27500}{1 + \frac{10}{e^{2.72}}}]$

Step 1.3

Write $1$ as a fraction with a common denominator.

$\frac{d}{d x} [\frac{27500}{\frac{e^{2.72}}{e^{2.72}} + \frac{10}{e^{2.72}}}]$

Step 1.4

Combine the numerators over the common denominator.

$\frac{d}{d x} [\frac{27500}{\frac{e^{2.72} + 10}{e^{2.72}}}]$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{d}{d x} [27500 \frac{e^{2.72}}{e^{2.72} + 10}]$

Step 3

Combine $27500$ and $\frac{e^{2.72}}{e^{2.72} + 10}$ .

$\frac{d}{d x} [\frac{27500 e^{2.72}}{e^{2.72} + 10}]$

Step 4

Since $\frac{27500 e^{2.72}}{e^{2.72} + 10}$ is constant with respect to $x$ , the derivative of $\frac{27500 e^{2.72}}{e^{2.72} + 10}$ with respect to $x$ is $0$ .

$0$