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

The derivative of x/(sqrt(x-4)) is (x-8)/(2(x-4)sqrt(x-4))

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

The first derivative of x/(sqrt(x-4)) is (x-8)/(2(x-4)sqrt(x-4))

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

\frac{x - 8}{2 ( x - 4 ) x - 4}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

\frac{1 \cdot x - 4 - \frac{1}{2 x - 4} x}{( x - 4 ) ^{2}} : \frac{x - 8}{2 ( x - 4 ) x - 4}

= \frac{x - 8}{2 ( x - 4 ) x - 4}

What is the derivative of x/(sqrt(x-4)) ?
The derivative of x/(sqrt(x-4)) is (x-8)/(2(x-4)sqrt(x-4))
What is the first derivative of x/(sqrt(x-4)) ?
The first derivative of x/(sqrt(x-4)) is (x-8)/(2(x-4)sqrt(x-4))