Calculus Examples

$f (x) = 1000 (50 - 3 p)$

Step 1

Since $1000$ is constant with respect to $p$ , the derivative of $1000 (50 - 3 p)$ with respect to $p$ is $1000 \frac{d}{d p} [50 - 3 p]$ .

$1000 \frac{d}{d p} [50 - 3 p]$

Step 2

By the Sum Rule, the derivative of $50 - 3 p$ with respect to $p$ is $\frac{d}{d p} [50] + \frac{d}{d p} [- 3 p]$ .

$1000 (\frac{d}{d p} [50] + \frac{d}{d p} [- 3 p])$

Step 3

Since $50$ is constant with respect to $p$ , the derivative of $50$ with respect to $p$ is $0$ .

$1000 (0 + \frac{d}{d p} [- 3 p])$

Step 4

Add $0$ and $\frac{d}{d p} [- 3 p]$ .

$1000 \frac{d}{d p} [- 3 p]$

Step 5

Since $- 3$ is constant with respect to $p$ , the derivative of $- 3 p$ with respect to $p$ is $- 3 \frac{d}{d p} [p]$ .

$1000 (- 3 \frac{d}{d p} [p])$

Step 6

Multiply $- 3$ by $1000$ .

$- 3000 \frac{d}{d p} [p]$

Step 7

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

$- 3000 \cdot 1$

Step 8

Multiply $- 3000$ by $1$ .

$- 3000$