What is the derivative of y=(2x+4)/(1-x) ?

The derivative of y=(2x+4)/(1-x) is 6/((1-x)^2)

What is the first derivative of y=(2x+4)/(1-x) ?

The first derivative of y=(2x+4)/(1-x) is 6/((1-x)^2)

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derivative

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (2 x + 4) = 2

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

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

Simplify

\frac{2 ( 1 - x ) - ( - 1 ) ( 2 x + 4 )}{( 1 - x ) ^{2}} : \frac{6}{( 1 - x ) ^{2}}

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

What is the derivative of y=(2x+4)/(1-x) ?
The derivative of y=(2x+4)/(1-x) is 6/((1-x)^2)
What is the first derivative of y=(2x+4)/(1-x) ?
The first derivative of y=(2x+4)/(1-x) is 6/((1-x)^2)