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

The derivative of f(x)=(x+2)e^{-x} is -e^{-x}x-e^{-x}

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

The first derivative of f(x)=(x+2)e^{-x} is -e^{-x}x-e^{-x}

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derivative of

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

- e^{- x} x - e^{- x}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= - e^{- x} x - e^{- x}

\int \frac{x}{27 + x ^{2}} d x

\frac{d}{d t} (2 t e^{t})

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

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

y^{^{'}} - y = 9 t

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