What is the derivative of (2sqrt(x))/(x^2-8) ?

The derivative of (2sqrt(x))/(x^2-8) is (-3x^2-8)/(sqrt(x)(x^2-8)^2)

What is the first derivative of (2sqrt(x))/(x^2-8) ?

The first derivative of (2sqrt(x))/(x^2-8) is (-3x^2-8)/(sqrt(x)(x^2-8)^2)

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derivative of

\frac{2 x}{x ^{2} - 8}

\frac{- 3 x ^{2} - 8}{x ( x ^{2} - 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x}{x ^{2} - 8})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (\frac{x}{x ^{2} - 8})

Apply the Quotient Rule:

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

= 2 \cdot \frac{\frac{d}{d x} ( x ) ( x ^{2} - 8 ) - \frac{d}{d x} ( x ^{2} - 8 ) x}{( x ^{2} - 8 ) ^{2}}

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (x^{2} - 8) = 2 x

= 2 \cdot \frac{\frac{1}{2 x} ( x ^{2} - 8 ) - 2 x x}{( x ^{2} - 8 ) ^{2}}

Simplify

2 \cdot \frac{\frac{1}{2 x} ( x ^{2} - 8 ) - 2 x x}{( x ^{2} - 8 ) ^{2}} : \frac{- 3 x ^{2} - 8}{x ( x ^{2} - 8 ) ^{2}}

= \frac{- 3 x ^{2} - 8}{x ( x ^{2} - 8 ) ^{2}}

What is the derivative of (2sqrt(x))/(x^2-8) ?
The derivative of (2sqrt(x))/(x^2-8) is (-3x^2-8)/(sqrt(x)(x^2-8)^2)
What is the first derivative of (2sqrt(x))/(x^2-8) ?
The first derivative of (2sqrt(x))/(x^2-8) is (-3x^2-8)/(sqrt(x)(x^2-8)^2)