Calculus Examples

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

Step 1

Cancel the common factor of $x^{3}$ and $x^{2}$ .

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Step 1.1

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

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

Multiply by $1$ .

$\frac{d}{d x} [\frac{x^{2} (2 x)}{x^{2} \cdot 1}]$

Step 1.2.2

Cancel the common factor.

$\frac{d}{d x} [\frac{x^{2} (2 x)}{x^{2} \cdot 1}]$

Step 1.2.3

Rewrite the expression.

$\frac{d}{d x} [\frac{2 x}{1}]$

Step 1.2.4

Divide $2 x$ by $1$ .

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

Step 2

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

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

Step 3

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

$2 \cdot 1$

Step 4

Multiply $2$ by $1$ .

$2$