Calculus Examples

$D_{x} (\frac{2 x + 5}{x^{2} - 1})$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $1$ as $1^{2}$ .

$\frac{d}{d D[x]} [D_{x} \frac{2 x + 5}{x^{2} - 1^{2}}]$

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

$\frac{d}{d D[x]} [D_{x} \frac{2 x + 5}{(x + 1) (x - 1)}]$

Step 2

Combine $D_{x}$ and $\frac{2 x + 5}{(x + 1) (x - 1)}$ .

$\frac{d}{d D[x]} [\frac{D_{x} (2 x + 5)}{(x + 1) (x - 1)}]$

Step 3

Since $\frac{D_{x} (2 x + 5)}{(x + 1) (x - 1)}$ is constant with respect to $D[x]$ , the derivative of $\frac{D_{x} (2 x + 5)}{(x + 1) (x - 1)}$ with respect to $D[x]$ is $0$ .

$0$