What is the derivative of y=(sqrt(x)-4)/(sqrt(x)+4) ?

The derivative of y=(sqrt(x)-4)/(sqrt(x)+4) is 4/(sqrt(x)(\sqrt{x)+4)^2}

What is the first derivative of y=(sqrt(x)-4)/(sqrt(x)+4) ?

The first derivative of y=(sqrt(x)-4)/(sqrt(x)+4) is 4/(sqrt(x)(\sqrt{x)+4)^2}

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derivative of

y = \frac{x - 4}{x + 4}

\frac{4}{x ( x + 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 4}{x + 4})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 4 ) ( x + 4 ) - \frac{d}{d x} ( x + 4 ) ( x - 4 )}{( x + 4 ) ^{2}}

\frac{d}{d x} (x - 4) = \frac{1}{2 x}

\frac{d}{d x} (x + 4) = \frac{1}{2 x}

= \frac{\frac{1}{2 x} ( x + 4 ) - \frac{1}{2 x} ( x - 4 )}{( x + 4 ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( x + 4 ) - \frac{1}{2 x} ( x - 4 )}{( x + 4 ) ^{2}} : \frac{4}{x ( x + 4 ) ^{2}}

= \frac{4}{x ( x + 4 ) ^{2}}

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\int_{6}^{8} \frac{78}{( x - 6 ) ^{3}} d x

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What is the derivative of y=(sqrt(x)-4)/(sqrt(x)+4) ?
The derivative of y=(sqrt(x)-4)/(sqrt(x)+4) is 4/(sqrt(x)(\sqrt{x)+4)^2}
What is the first derivative of y=(sqrt(x)-4)/(sqrt(x)+4) ?
The first derivative of y=(sqrt(x)-4)/(sqrt(x)+4) is 4/(sqrt(x)(\sqrt{x)+4)^2}