What is the derivative of sqrt(x/(x+1)) ?

The derivative of sqrt(x/(x+1)) is 1/(2sqrt(x)(x+1)^{3/2)}

What is the first derivative of sqrt(x/(x+1)) ?

The first derivative of sqrt(x/(x+1)) is 1/(2sqrt(x)(x+1)^{3/2)}

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derivative of

\frac{x}{x + 1}

\frac{1}{2 x ( x + 1 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{x}{x + 1})

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{2 x ( x + 1 ) ^{\frac{3}{2}}}

What is the derivative of sqrt(x/(x+1)) ?
The derivative of sqrt(x/(x+1)) is 1/(2sqrt(x)(x+1)^{3/2)}
What is the first derivative of sqrt(x/(x+1)) ?
The first derivative of sqrt(x/(x+1)) is 1/(2sqrt(x)(x+1)^{3/2)}