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Popular >

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

Solution

derivative of

g (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 cos (4 θ) 2 - sin (4 θ) d θ

sum from k=1 to infinity of 1/(k+2)

k = 1 \sum \infty \frac{1}{k + 2}

derivative of sqrt(1+3x)derivative of

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laplacetransform e^{1-2t}laplace transform

e^{1 - 2 t}

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\frac{d}{d x} (\frac{2 x ^{3} - 6 π ^{2}}{x ^{5}})

Frequently Asked Questions (FAQ)

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