What is the derivative of (x^2+1/((x+1)^3)) ?

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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