What is the derivative of x/(sqrt(x^2-4)) ?

The derivative of x/(sqrt(x^2-4)) is -4/((x^2-4)sqrt(x^2-4))

What is the first derivative of x/(sqrt(x^2-4)) ?

The first derivative of x/(sqrt(x^2-4)) is -4/((x^2-4)sqrt(x^2-4))

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\frac{d}{d x} (\frac{x}{x ^{2} - 4})

- \frac{4}{( x ^{2} - 4 ) x ^{2} - 4}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} - 4})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d x}{d x} x ^{2} - 4 - \frac{d}{d x} ( x ^{2} - 4 ) x}{( x ^{2} - 4 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{2} - 4) = \frac{x}{x ^{2} - 4}

= \frac{1 \cdot x ^{2} - 4 - \frac{x}{x ^{2} - 4} x}{( x ^{2} - 4 ) ^{2}}

Simplify

\frac{1 \cdot x ^{2} - 4 - \frac{x}{x ^{2} - 4} x}{( x ^{2} - 4 ) ^{2}} : - \frac{4}{( x ^{2} - 4 ) x ^{2} - 4}

= - \frac{4}{( x ^{2} - 4 ) x ^{2} - 4}

(π)^{^{'}}

x \to 0 lim (\frac{1}{x} + 1)

\int \frac{x}{1 - x ^{8}} d x

f (x) = cos (x^{2}) 2 x

\int 8 x^{- 1} d x

What is the derivative of x/(sqrt(x^2-4)) ?
The derivative of x/(sqrt(x^2-4)) is -4/((x^2-4)sqrt(x^2-4))
What is the first derivative of x/(sqrt(x^2-4)) ?
The first derivative of x/(sqrt(x^2-4)) is -4/((x^2-4)sqrt(x^2-4))