What is the derivative of (sqrt(x)+1/(sqrt(x)+2)) ?

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

What is the first derivative of (sqrt(x)+1/(sqrt(x)+2)) ?

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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