What is the derivative of ((x+2^2)/(1-x)) ?

The derivative of ((x+2^2)/(1-x)) is (-x^2+2x+8)/((1-x)^2)

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

The first derivative of ((x+2^2)/(1-x)) is (-x^2+2x+8)/((1-x)^2)

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

\frac{- x ^{2} + 2 x + 8}{( 1 - x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 ( x + 2 ) ( 1 - x ) - ( - 1 ) ( x + 2 ) ^{2}}{( 1 - x ) ^{2}} : \frac{- x ^{2} + 2 x + 8}{( 1 - x ) ^{2}}

= \frac{- x ^{2} + 2 x + 8}{( 1 - x ) ^{2}}

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

\frac{d}{d x} (ln (x^{2} + 3 x + 5))

\int 10 x^{4} d x

y = 25 - x^{2}, (0, 5)

(t^{2} + 9) e^{t}

What is the derivative of ((x+2^2)/(1-x)) ?
The derivative of ((x+2^2)/(1-x)) is (-x^2+2x+8)/((1-x)^2)
What is the first derivative of ((x+2^2)/(1-x)) ?
The first derivative of ((x+2^2)/(1-x)) is (-x^2+2x+8)/((1-x)^2)