What is the derivative of f(x)=((sqrt(x))/(x+1))^2 ?

The derivative of f(x)=((sqrt(x))/(x+1))^2 is (-x+1)/((x+1)^3)

What is the first derivative of f(x)=((sqrt(x))/(x+1))^2 ?

The first derivative of f(x)=((sqrt(x))/(x+1))^2 is (-x+1)/((x+1)^3)

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial y} (e^{x} (1 - cos (y)))

\frac{4}{s - 2}

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

x \to - 2 lim (2 x + 3)

What is the derivative of f(x)=((sqrt(x))/(x+1))^2 ?
The derivative of f(x)=((sqrt(x))/(x+1))^2 is (-x+1)/((x+1)^3)
What is the first derivative of f(x)=((sqrt(x))/(x+1))^2 ?
The first derivative of f(x)=((sqrt(x))/(x+1))^2 is (-x+1)/((x+1)^3)