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

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

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

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

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

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

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

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

Simplify

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

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

\int \frac{4 x - 6}{x ^{2} + 4} d x

\int \frac{3}{2} x^{2} d x

\int \frac{1}{x ^{3} - 2 x ^{2} + x} d x

\frac{\partial}{\partial y} (2 z)

\frac{2 x}{x ^{2} + 1}

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