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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

2 (x + 1) (x^{2} + 1) - 2 x (x + 1)^{2} : - 2 x^{2} + 2

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

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