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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

Simplify

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

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

y = 3 x, y = 3 x

\frac{\partial}{\partial y} (22 cos (x) y z^{2})

x - x^{2}

\int 8 x + 6 d x

\frac{\partial}{\partial y} ((y - 5) (x + 5)^{2})

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