What is the derivative of x/(sqrt(9-4x)) ?

The derivative of x/(sqrt(9-4x)) is (9-2x)/((9-4x)sqrt(9-4x))

What is the first derivative of x/(sqrt(9-4x)) ?

The first derivative of x/(sqrt(9-4x)) is (9-2x)/((9-4x)sqrt(9-4x))

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\frac{d}{d x} (\frac{x}{9 - 4 x})

\frac{9 - 2 x}{( 9 - 4 x ) 9 - 4 x}

Solution steps

\frac{d}{d x} (\frac{x}{9 - 4 x})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} 9 - 4 x - \frac{d}{d x} ( 9 - 4 x ) x}{( 9 - 4 x ) ^{2}}

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

\frac{d}{d x} (9 - 4 x) = - \frac{2}{9 - 4 x}

= \frac{1 \cdot 9 - 4 x - ( - \frac{2}{9 - 4 x} ) x}{( 9 - 4 x ) ^{2}}

Simplify

\frac{1 \cdot 9 - 4 x - ( - \frac{2}{9 - 4 x} ) x}{( 9 - 4 x ) ^{2}} : \frac{9 - 2 x}{( 9 - 4 x ) 9 - 4 x}

= \frac{9 - 2 x}{( 9 - 4 x ) 9 - 4 x}

What is the derivative of x/(sqrt(9-4x)) ?
The derivative of x/(sqrt(9-4x)) is (9-2x)/((9-4x)sqrt(9-4x))
What is the first derivative of x/(sqrt(9-4x)) ?
The first derivative of x/(sqrt(9-4x)) is (9-2x)/((9-4x)sqrt(9-4x))