Calculus Examples

$q = 887 - 9 p$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d p} (q) = \frac{d}{d p} (887 - 9 p)$

Step 2

The derivative of $q$ with respect to $p$ is $q'$ .

$q'$

Step 3

Differentiate the right side of the equation.

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Step 3.1

Differentiate.

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Step 3.1.1

By the Sum Rule, the derivative of $887 - 9 p$ with respect to $p$ is $\frac{d}{d p} [887] + \frac{d}{d p} [- 9 p]$ .

$\frac{d}{d p} [887] + \frac{d}{d p} [- 9 p]$

Step 3.1.2

Since $887$ is constant with respect to $p$ , the derivative of $887$ with respect to $p$ is $0$ .

$0 + \frac{d}{d p} [- 9 p]$

Step 3.2

Evaluate $\frac{d}{d p} [- 9 p]$ .

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Step 3.2.1

Since $- 9$ is constant with respect to $p$ , the derivative of $- 9 p$ with respect to $p$ is $- 9 \frac{d}{d p} [p]$ .

$0 - 9 \frac{d}{d p} [p]$

Step 3.2.2

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

$0 - 9 \cdot 1$

Step 3.2.3

Multiply $- 9$ by $1$ .

$0 - 9$

Step 3.3

Subtract $9$ from $0$ .

$- 9$

Step 4

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

$q' = - 9$

Step 5

Replace $q'$ with $\frac{d q}{d p}$ .

$\frac{d q}{d p} = - 9$