Calculus Examples

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

Step 1

Since $\frac{1}{4 x^{2}}$ is constant with respect to $y$ , the derivative of $\frac{y^{2}}{4 x^{2}}$ with respect to $y$ is $\frac{1}{4 x^{2}} \frac{d}{d y} [y^{2}]$ .

$\frac{1}{4 x^{2}} \frac{d}{d y} [y^{2}]$

Step 2

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

$\frac{1}{4 x^{2}} (2 y)$

Step 3

Simplify terms.

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Step 3.1

Combine $2$ and $\frac{1}{4 x^{2}}$ .

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

Step 3.2

Combine $\frac{2}{4 x^{2}}$ and $y$ .

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

Step 3.3

Cancel the common factor of $2$ and $4$ .

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Step 3.3.1

Factor $2$ out of $2 y$ .

$\frac{2 (y)}{4 x^{2}}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $2$ out of $4 x^{2}$ .

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

Step 3.3.2.2

Cancel the common factor.

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

Step 3.3.2.3

Rewrite the expression.

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