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}}}

n = 1 \sum \infty n \cdot x^{n}

\frac{d}{d x} (2 - 2 cos (x))

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

\frac{\partial}{\partial x} (e^{5 x y})

\int \frac{1}{1 + 4 t ^{2}} d t

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)}