Calculus Examples

$f (x) = 2 - \frac{2}{3} x$

Step 1

Differentiate.

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Step 1.1

By the Sum Rule, the derivative of $2 - \frac{2}{3} x$ with respect to $x$ is $\frac{d}{d x} [2] + \frac{d}{d x} [- \frac{2}{3} x]$ .

$\frac{d}{d x} [2] + \frac{d}{d x} [- \frac{2}{3} x]$

Step 1.2

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

$0 + \frac{d}{d x} [- \frac{2}{3} x]$

Step 2

Evaluate $\frac{d}{d x} [- \frac{2}{3} x]$ .

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Step 2.1

Since $- \frac{2}{3}$ is constant with respect to $x$ , the derivative of $- \frac{2}{3} x$ with respect to $x$ is $- \frac{2}{3} \frac{d}{d x} [x]$ .

$0 - \frac{2}{3} \frac{d}{d x} [x]$

Step 2.2

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

$0 - \frac{2}{3} \cdot 1$

Step 2.3

Multiply $- 1$ by $1$ .

$0 - \frac{2}{3}$

Step 3

Subtract $\frac{2}{3}$ from $0$ .

$- \frac{2}{3}$