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Popular Calculus >

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

Solution

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

Solution

- e^{- x} x^{2} + e^{- x} x

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2} + x + 1, g = e^{- x}

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

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

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

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

Simplify

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

= - e^{- x} x^{2} + e^{- x} x

Graph

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

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Frequently Asked Questions (FAQ)

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