What is the derivative of x/(sqrt(x-3)) ?

The derivative of x/(sqrt(x-3)) is (x-6)/(2(x-3)sqrt(x-3))

What is the first derivative of x/(sqrt(x-3)) ?

The first derivative of x/(sqrt(x-3)) is (x-6)/(2(x-3)sqrt(x-3))

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\frac{d}{d x} (\frac{x}{x - 3})

\frac{x - 6}{2 ( x - 3 ) x - 3}

Solution steps

\frac{d}{d x} (\frac{x}{x - 3})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} x - 3 - \frac{d}{d x} ( x - 3 ) x}{( x - 3 ) ^{2}}

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

\frac{d}{d x} (x - 3) = \frac{1}{2 x - 3}

= \frac{1 \cdot x - 3 - \frac{1}{2 x - 3} x}{( x - 3 ) ^{2}}

Simplify

\frac{1 \cdot x - 3 - \frac{1}{2 x - 3} x}{( x - 3 ) ^{2}} : \frac{x - 6}{2 ( x - 3 ) x - 3}

= \frac{x - 6}{2 ( x - 3 ) x - 3}

What is the derivative of x/(sqrt(x-3)) ?
The derivative of x/(sqrt(x-3)) is (x-6)/(2(x-3)sqrt(x-3))
What is the first derivative of x/(sqrt(x-3)) ?
The first derivative of x/(sqrt(x-3)) is (x-6)/(2(x-3)sqrt(x-3))