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 x e^{9 - x^{2}} d x

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

\int (x - 5) ln (x) d x

\int \frac{e ^{\frac{1}{z}}}{z ^{2}} d z

y = 3 - 4 x^{2}, (- 1, - 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}