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Popular Calculus >

derivative of ((sqrt(x)-5))/(sqrt(x)+5)

Solution

derivative of

\frac{( x - 5 )}{x + 5}

Solution

\frac{5}{x ( x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 5}{x + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 5 ) ( x + 5 ) - \frac{d}{d x} ( x + 5 ) ( x - 5 )}{( x + 5 ) ^{2}}

\frac{d}{d x} (x - 5) = \frac{1}{2 x}

\frac{d}{d x} (x + 5) = \frac{1}{2 x}

= \frac{\frac{1}{2 x} ( x + 5 ) - \frac{1}{2 x} ( x - 5 )}{( x + 5 ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( x + 5 ) - \frac{1}{2 x} ( x - 5 )}{( x + 5 ) ^{2}} : \frac{5}{x ( x + 5 ) ^{2}}

= \frac{5}{x ( x + 5 ) ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ((sqrt(x)-5))/(sqrt(x)+5) ?
The derivative of ((sqrt(x)-5))/(sqrt(x)+5) is 5/(sqrt(x)(\sqrt{x)+5)^2}
What is the first derivative of ((sqrt(x)-5))/(sqrt(x)+5) ?
The first derivative of ((sqrt(x)-5))/(sqrt(x)+5) is 5/(sqrt(x)(\sqrt{x)+5)^2}