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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x \to 1 lim (cot (\frac{π}{2} x))

(sin (x))^{(87)}

\int (z^{2} + z)^{2} d z

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

\frac{1}{( s ^{2} + 2 s + 2 ) ( s ^{2} + 9 )}

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