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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{( t + 2 t ^{2} )}{1 + t ^{2}}

5 + 6 x

n = 0 \sum \infty \frac{( x ^{n} )}{n !}

\int x^{14} d x

\int cos (\frac{π}{2}) x d x

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