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}}

\int 7 d x

\int sin^{2} (x) - sin^{3} (x) d x

\frac{450}{s ( s + 3 ) ^{2}}

y = x^{x} + 1

t \to 0 lim (\frac{2}{t} - \frac{2}{t ^{2} + t})

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}