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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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