Calculus Examples

$y = \frac{11 x^{2}}{4 x}$

Step 1

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

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Step 1.1

Factor $x$ out of $11 x^{2}$ .

$\frac{d}{d x} [\frac{x (11 x)}{4 x}]$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $x$ out of $4 x$ .

$\frac{d}{d x} [\frac{x (11 x)}{x \cdot 4}]$

Step 1.2.2

Cancel the common factor.

$\frac{d}{d x} [\frac{x (11 x)}{x \cdot 4}]$

Step 1.2.3

Rewrite the expression.

$\frac{d}{d x} [\frac{11 x}{4}]$

Step 2

Since $\frac{11}{4}$ is constant with respect to $x$ , the derivative of $\frac{11 x}{4}$ with respect to $x$ is $\frac{11}{4} \frac{d}{d x} [x]$ .

$\frac{11}{4} \frac{d}{d x} [x]$

Step 3

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

$\frac{11}{4} \cdot 1$

Step 4

Multiply $\frac{11}{4}$ by $1$ .

$\frac{11}{4}$