Calculus Examples

$\frac{d}{d x} (\frac{x^{3}}{12})$

Step 1

This derivative could not be completed using the chain rule. Mathway will use another method.

Step 2

Since $\frac{1}{12}$ is constant with respect to $x$ , the derivative of $\frac{x^{3}}{12}$ with respect to $x$ is $\frac{1}{12} \frac{d}{d x} [x^{3}]$ .

$\frac{1}{12} \frac{d}{d x} [x^{3}]$

Step 3

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 3$ .

$\frac{1}{12} (3 x^{2})$

Step 4

Simplify terms.

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Step 4.1

Combine $3$ and $\frac{1}{12}$ .

$\frac{3}{12} x^{2}$

Step 4.2

Combine $\frac{3}{12}$ and $x^{2}$ .

$\frac{3 x^{2}}{12}$

Step 4.3

Cancel the common factor of $3$ and $12$ .

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Step 4.3.1

Factor $3$ out of $3 x^{2}$ .

$\frac{3 (x^{2})}{12}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $3$ out of $12$ .

$\frac{3 x^{2}}{3 \cdot 4}$

Step 4.3.2.2

Cancel the common factor.

$\frac{3 x^{2}}{3 \cdot 4}$

Step 4.3.2.3

Rewrite the expression.

$\frac{x^{2}}{4}$