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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

Simplify

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

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

y^{^{''}} + 30 y = 0

\int \frac{2 x}{2 x - 1} d x

\int (2 x^{3} - x + 0)^{3} \cdot (6 x^{2} - 1) d x

\frac{d}{d x} (6^{x})

\int x e^{- 0.5 x^{2}} d x

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