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

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

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

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

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derivative of

y = \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}}

f (x) = 7 x e^{x}, at x = 0

\frac{d}{d x} (5 x^{\frac{3}{5}} - 4)

y = \frac{6 + x f ( x )}{x}

\int y^{2} 2 y^{3} + 1 d y

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

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