What is the derivative of ((2+x))/((2-x)) ?

The derivative of ((2+x))/((2-x)) is 4/((2-x)^2)

What is the first derivative of ((2+x))/((2-x)) ?

The first derivative of ((2+x))/((2-x)) is 4/((2-x)^2)

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derivative of

\frac{( 2 + x )}{( 2 - x )}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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