Calculus Examples

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

Step 1

Since $\frac{1}{y}$ is constant with respect to $x$ , the derivative of $\frac{x^{2}}{y}$ with respect to $x$ is $\frac{1}{y} \frac{d}{d x} [x^{2}]$ .

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

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

$\frac{1}{y} (2 x)$

Step 3

Combine fractions.

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Step 3.1

Combine $2$ and $\frac{1}{y}$ .

$\frac{2}{y} x$

Step 3.2

Combine $\frac{2}{y}$ and $x$ .

$\frac{2 x}{y}$