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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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

4 x ln (2 x + 1)

\frac{d}{d q} (2600 - 13 q)

cos (x) + 1

\frac{1}{( a - x )}

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