What is the derivative of (3x/(sqrt(1-x))) ?

The derivative of (3x/(sqrt(1-x))) is (3(2-x))/(2(1-x)sqrt(1-x))

What is the first derivative of (3x/(sqrt(1-x))) ?

The first derivative of (3x/(sqrt(1-x))) is (3(2-x))/(2(1-x)sqrt(1-x))

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int \frac{( x ^{\frac{1}{3}} )}{x ^{\frac{2}{3}}} d x

\int \frac{1}{( 8 - 2 x - x ^{2} ) ^{\frac{3}{2}}} d x

n = 0 \sum \infty \frac{2 ^{n}}{4 ^{n}}

\int (4 x^{2} - 5 x)^{5} (8 x - 5) d x

\int_{- \infty}^{1} 2^{x} d x

What is the derivative of (3x/(sqrt(1-x))) ?
The derivative of (3x/(sqrt(1-x))) is (3(2-x))/(2(1-x)sqrt(1-x))
What is the first derivative of (3x/(sqrt(1-x))) ?
The first derivative of (3x/(sqrt(1-x))) is (3(2-x))/(2(1-x)sqrt(1-x))