# Step-by-step Solution

## Find the derivative using the quotient rule $\frac{d}{dx}\left(\frac{x^2}{x^2-4}\right)$

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### Videos

$\frac{2x\left(x^2-4\right)-2x^{3}}{\left(x^2-4\right)^2}$

## Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(\frac{x^2}{x^2-4}\right)$
1

Applying the quotient rule which states that if $f(x)$ and $g(x)$ are functions and $h(x)$ is the function defined by $h(x) = \frac{f(x)}{g(x)}$, where ${g(x) \neq 0}$, then $h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}$

$\frac{\left(x^2-4\right)\frac{d}{dx}\left(x^2\right)-x^2\frac{d}{dx}\left(x^2-4\right)}{\left(x^2-4\right)^2}$
2

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$\frac{2x\left(x^2-4\right)-x^2\frac{d}{dx}\left(x^2-4\right)}{\left(x^2-4\right)^2}$

$\frac{2x\left(x^2-4\right)-2x^{3}}{\left(x^2-4\right)^2}$
$\frac{d}{dx}\left(\frac{x^2}{x^2-4}\right)$