Calculus Examples

$B = P e^{r t}$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d P} (B) = \frac{d}{d P} (P e^{r t})$

Step 2

The derivative of $B$ with respect to $P$ is $B'$ .

$B'$

Step 3

Differentiate the right side of the equation.

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

$e^{r t} \frac{d}{d P} [P]$

Differentiate using the Power Rule which states that $\frac{d}{d P} [P^{n}]$ is $n P^{n - 1}$ where $n = 1$ .

$e^{r t} \cdot 1$

Multiply $e^{r t}$ by $1$ .

$e^{r t}$

Step 4

Reform the equation by setting the left side equal to the right side.

$B' = e^{r t}$

Step 5

Replace $B'$ with $\frac{d B}{d P}$ .

$\frac{d B}{d P} = e^{r t}$