What is the derivative of (-6x/(1-x)) ?

The derivative of (-6x/(1-x)) is -6/((1-x)^2)

What is the first derivative of (-6x/(1-x)) ?

The first derivative of (-6x/(1-x)) is -6/((1-x)^2)

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\frac{d}{d x} (\frac{- 6 x}{1 - x})

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

Solution steps

\frac{d}{d x} (\frac{- 6 x}{1 - x})

Simplify

\frac{- 6 x}{1 - x} : - \frac{6 x}{1 - x}

= \frac{d}{d x} (- \frac{6 x}{1 - x})

Take the constant out:

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

= - 6 \frac{d}{d x} (\frac{x}{1 - x})

Apply the Quotient Rule:

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

= - 6 \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) = - 1

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

Simplify

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

= - \frac{6}{( 1 - x ) ^{2}}

\frac{s + 4}{s ^{2} + 6 s + 18}

\int a x^{5} d x

y = x^{2}, y = 8 - x^{2}, y = 4 x + 11

x \to 3 lim ((x - 2)^{2})

\frac{d y}{d x} = \frac{k}{x ^{2}}

What is the derivative of (-6x/(1-x)) ?
The derivative of (-6x/(1-x)) is -6/((1-x)^2)
What is the first derivative of (-6x/(1-x)) ?
The first derivative of (-6x/(1-x)) is -6/((1-x)^2)