Calculus Examples

$2 p$

Step 1

Find the first derivative.

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Step 1.1

Since $2$ is constant with respect to $p$ , the derivative of $2 p$ with respect to $p$ is $2 \frac{d}{d p} [p]$ .

$2 \frac{d}{d p} [p]$

Step 1.2

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

$2 \cdot 1$

Step 1.3

Multiply $2$ by $1$ .

$f' (p) = 2$

Step 2

Since $2$ is constant with respect to $p$ , the derivative of $2$ with respect to $p$ is $0$ .

$f'' (p) = 0$

Step 3

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

$f''' (p) = 0$

Step 4

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

$f^{4} (p) = 0$