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

Simplify

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

\int x + 5 d x

\frac{- x ^{2}}{2}

\frac{d}{d x} (- 8 e^{- 4 x^{2}} x)

\int \frac{1}{1 + e ^{- y}} d y

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)