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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (1 - x) = - 1

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

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

Simplify

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

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

x (3 x - 2)

x \to \infty + lim (\frac{1}{x} + x)

\int \frac{e ^{5 t}}{t} d t

\frac{d ^{2} y}{d x ^{2}} + 64 y = 0

\frac{\partial}{\partial x} (1 - x^{7} - y^{7})

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