Calculus Examples

$\frac{k n}{1 + n^{2}}$

Step 1

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

$\frac{n}{1 + n^{2}} \frac{d}{d k} [k]$

Step 2

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

$\frac{n}{1 + n^{2}} \cdot 1$

Step 3

Simplify the expression.

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Step 3.1

Multiply $\frac{n}{1 + n^{2}}$ by $1$ .

$\frac{n}{1 + n^{2}}$

Step 3.2

Reorder terms.

$\frac{n}{n^{2} + 1}$