Calculus Examples

$f (x) = \frac{4 x^{2} - 2 x^{2}}{2 x}$

Step 1

Simplify terms.

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Step 1.1

Subtract $2 x^{2}$ from $4 x^{2}$ .

$\frac{d}{d x} [\frac{2 x^{2}}{2 x}]$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Cancel the common factor.

$\frac{d}{d x} [\frac{2 x^{2}}{2 x}]$

Step 1.2.2

Rewrite the expression.

$\frac{d}{d x} [\frac{x^{2}}{x}]$

Step 1.3

Cancel the common factor of $x^{2}$ and $x$ .

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Step 1.3.1

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

$\frac{d}{d x} [\frac{x \cdot x}{x}]$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Raise $x$ to the power of $1$ .

$\frac{d}{d x} [\frac{x \cdot x}{x^{1}}]$

Step 1.3.2.2

Factor $x$ out of $x^{1}$ .

$\frac{d}{d x} [\frac{x \cdot x}{x \cdot 1}]$

Step 1.3.2.3

Cancel the common factor.

$\frac{d}{d x} [\frac{x \cdot x}{x \cdot 1}]$

Step 1.3.2.4

Rewrite the expression.

$\frac{d}{d x} [\frac{x}{1}]$

Step 1.3.2.5

Divide $x$ by $1$ .

$\frac{d}{d x} [x]$

Step 2

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

$1$