Calculus Examples

$\frac{7}{3} \cdot (9 x + 3)$

Step 1

Since $\frac{7}{3}$ is constant with respect to $x$ , the derivative of $\frac{7}{3} (9 x + 3)$ with respect to $x$ is $\frac{7}{3} \frac{d}{d x} [9 x + 3]$ .

$\frac{7}{3} \frac{d}{d x} [9 x + 3]$

Step 2

By the Sum Rule, the derivative of $9 x + 3$ with respect to $x$ is $\frac{d}{d x} [9 x] + \frac{d}{d x} [3]$ .

$\frac{7}{3} (\frac{d}{d x} [9 x] + \frac{d}{d x} [3])$

Step 3

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

$\frac{7}{3} (9 \frac{d}{d x} [x] + \frac{d}{d x} [3])$

Step 4

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

$\frac{7}{3} (9 \cdot 1 + \frac{d}{d x} [3])$

Step 5

Multiply $9$ by $1$ .

$\frac{7}{3} (9 + \frac{d}{d x} [3])$

Step 6

Since $3$ is constant with respect to $x$ , the derivative of $3$ with respect to $x$ is $0$ .

$\frac{7}{3} (9 + 0)$

Step 7

Simplify terms.

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Step 7.1

Add $9$ and $0$ .

$\frac{7}{3} \cdot 9$

Step 7.2

Combine $\frac{7}{3}$ and $9$ .

$\frac{7 \cdot 9}{3}$

Step 7.3

Multiply $7$ by $9$ .

$\frac{63}{3}$

Step 7.4

Cancel the common factor of $63$ and $3$ .

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Step 7.4.1

Factor $3$ out of $63$ .

$\frac{3 \cdot 21}{3}$

Step 7.4.2

Cancel the common factors.

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Step 7.4.2.1

Factor $3$ out of $3$ .

$\frac{3 \cdot 21}{3 (1)}$

Step 7.4.2.2

Cancel the common factor.

$\frac{3 \cdot 21}{3 \cdot 1}$

Step 7.4.2.3

Rewrite the expression.

$\frac{21}{1}$

Step 7.4.2.4

Divide $21$ by $1$ .

$21$