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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (y z e^{x})

\frac{d y}{d x} = x y + 2 x + 3 y + 6

7 x^{2}, at x = 10

y^{^{''}} + 4 y^{^{'}} + 4 y = 6 e^{- 2 x}

\int 20 x^{4} d x

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