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Popular >

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

Solution

derivative of

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

Solution

- 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}

Popular Examples

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\int 3 x cos (9 x) d x

tangent of f(x)=x^3-2x+1 tangent of

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

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\frac{d}{d x} (lo g_{3} (sec (x)))

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Frequently Asked Questions (FAQ)

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}