What is the derivative of (sqrt(x)+1/(sqrt(x)+5)) ?

The derivative of (sqrt(x)+1/(sqrt(x)+5)) is 2/(sqrt(x)(\sqrt{x)+5)^2}

What is the first derivative of (sqrt(x)+1/(sqrt(x)+5)) ?

The first derivative of (sqrt(x)+1/(sqrt(x)+5)) is 2/(sqrt(x)(\sqrt{x)+5)^2}

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\frac{d}{d x} (\frac{x + 1}{x + 5})

\frac{2}{x ( x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x + 1}{x + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 1 ) ( x + 5 ) - \frac{d}{d x} ( x + 5 ) ( x + 1 )}{( x + 5 ) ^{2}}

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

\frac{d}{d x} (x + 5) = \frac{1}{2 x}

= \frac{\frac{1}{2 x} ( x + 5 ) - \frac{1}{2 x} ( x + 1 )}{( x + 5 ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( x + 5 ) - \frac{1}{2 x} ( x + 1 )}{( x + 5 ) ^{2}} : \frac{2}{x ( x + 5 ) ^{2}}

= \frac{2}{x ( x + 5 ) ^{2}}

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What is the derivative of (sqrt(x)+1/(sqrt(x)+5)) ?
The derivative of (sqrt(x)+1/(sqrt(x)+5)) is 2/(sqrt(x)(\sqrt{x)+5)^2}
What is the first derivative of (sqrt(x)+1/(sqrt(x)+5)) ?
The first derivative of (sqrt(x)+1/(sqrt(x)+5)) is 2/(sqrt(x)(\sqrt{x)+5)^2}