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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Graph

Popular Examples

integral of (-2000x)/(sqrt(25-x^2))

\int \frac{- 2000 x}{25 - x ^{2}} d x

derivative of ln(arcsin(x))

\frac{d}{d x} (ln (arcsin (x)))

integral of-2y+4e^{-x}

\int - 2 y + 4 e^{- x} d x

integral from 2 to 4 of (2x-3)/6

\int_{2}^{4} \frac{2 x - 3}{6} d x

area y= 7/(16-x^2),[1,3]area

y = \frac{7}{16 - x ^{2}}, [1, 3]

Frequently Asked Questions (FAQ)

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