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

The derivative of (1-x/((x+1)^3)) is -(2(-x+2))/((x+1)^4)

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

The first derivative of (1-x/((x+1)^3)) is -(2(-x+2))/((x+1)^4)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( - 1 ) ( x + 1 ) ^{3} - 3 ( x + 1 ) ^{2} ( 1 - x )}{( ( x + 1 ) ^{3} ) ^{2}} : - \frac{2 ( - x + 2 )}{( x + 1 ) ^{4}}

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

What is the derivative of (1-x/((x+1)^3)) ?
The derivative of (1-x/((x+1)^3)) is -(2(-x+2))/((x+1)^4)
What is the first derivative of (1-x/((x+1)^3)) ?
The first derivative of (1-x/((x+1)^3)) is -(2(-x+2))/((x+1)^4)