What is the derivative of sqrt(x/(x^2+6)) ?

The derivative of sqrt(x/(x^2+6)) is (-x^2+6)/(2sqrt(x)(x^2+6)^{3/2)}

What is the first derivative of sqrt(x/(x^2+6)) ?

The first derivative of sqrt(x/(x^2+6)) is (-x^2+6)/(2sqrt(x)(x^2+6)^{3/2)}

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derivative of

\frac{x}{x ^{2} + 6}

\frac{- x ^{2} + 6}{2 x ( x ^{2} + 6 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} + 6})

Apply the chain rule:

\frac{1}{2 \frac{x}{x ^{2} + 6}} \frac{d}{d x} (\frac{x}{x ^{2} + 6})

= \frac{1}{2 \frac{x}{x ^{2} + 6}} \frac{d}{d x} (\frac{x}{x ^{2} + 6})

\frac{d}{d x} (\frac{x}{x ^{2} + 6}) = \frac{- x ^{2} + 6}{( x ^{2} + 6 ) ^{2}}

= \frac{1}{2 \frac{x}{x ^{2} + 6}} \cdot \frac{- x ^{2} + 6}{( x ^{2} + 6 ) ^{2}}

Simplify

\frac{1}{2 \frac{x}{x ^{2} + 6}} \cdot \frac{- x ^{2} + 6}{( x ^{2} + 6 ) ^{2}} : \frac{- x ^{2} + 6}{2 x ( x ^{2} + 6 ) ^{\frac{3}{2}}}

= \frac{- x ^{2} + 6}{2 x ( x ^{2} + 6 ) ^{\frac{3}{2}}}

[x - y arctan (\frac{y}{x})] d x + x arctan (\frac{y}{x}) d y = 0

\int_{7}^{\infty} x e^{- 2 x} d x

t y^{^{'}} + 2 y = t^{2}

x \to \infty lim (\frac{e ^{2 x - 7}}{6 x})

\int \frac{x ^{2} - 7}{7 x} d x

What is the derivative of sqrt(x/(x^2+6)) ?
The derivative of sqrt(x/(x^2+6)) is (-x^2+6)/(2sqrt(x)(x^2+6)^{3/2)}
What is the first derivative of sqrt(x/(x^2+6)) ?
The first derivative of sqrt(x/(x^2+6)) is (-x^2+6)/(2sqrt(x)(x^2+6)^{3/2)}