Calculus Examples

$g (t) = \frac{40000}{1 + 18 e^{- 0.51 \cdot 6}}$

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

Multiply $- 0.51$ by $6$ .

$\frac{d}{d x} [\frac{40000}{1 + 18 e^{- 3.06}}]$

Step 1.2

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

$\frac{d}{d x} [\frac{40000}{1 + 18 \frac{1}{e^{3.06}}}]$

Step 1.3

Combine $18$ and $\frac{1}{e^{3.06}}$ .

$\frac{d}{d x} [\frac{40000}{1 + \frac{18}{e^{3.06}}}]$

Step 1.4

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

$\frac{d}{d x} [\frac{40000}{\frac{e^{3.06}}{e^{3.06}} + \frac{18}{e^{3.06}}}]$

Step 1.5

Combine the numerators over the common denominator.

$\frac{d}{d x} [\frac{40000}{\frac{e^{3.06} + 18}{e^{3.06}}}]$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{d}{d x} [40000 \frac{e^{3.06}}{e^{3.06} + 18}]$

Step 3

Combine $40000$ and $\frac{e^{3.06}}{e^{3.06} + 18}$ .

$\frac{d}{d x} [\frac{40000 e^{3.06}}{e^{3.06} + 18}]$

Step 4

Since $\frac{40000 e^{3.06}}{e^{3.06} + 18}$ is constant with respect to $x$ , the derivative of $\frac{40000 e^{3.06}}{e^{3.06} + 18}$ with respect to $x$ is $0$ .

$0$