What is the derivative of (e^{-x}/(1+x^2)) ?

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

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

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

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

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

Solution steps

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

\frac{d}{d x} (e^{- x}) = - e^{- x}

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

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

Simplify

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

\int \frac{sec ( x )}{( sec ( x ) - tan ( x ) )} d x

y^{^{'}} + 2 x = 0

\frac{\partial}{\partial t} (s^{2} t^{2})

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

\frac{- 3 x - 2}{2 x ^{2} + x + 3}

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