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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derivative of

\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}}

\int sin^{8} (x) cos^{5} (x) d x

\frac{d}{d x} (\frac{e ^{x}}{- 8 x ^{7}})

x \to - \infty lim (5 x^{5} - 7 x^{4} + 1)

x cos^{2} (y) d x + tan (y) d y = 0

(1.1) (0.1)

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}