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

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

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

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

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derivative of

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

\int \frac{1}{2 x + 1} d x

f (x) = \frac{1}{2 x - 5}

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

3 x + 5

\frac{d y}{d t} = 4 y (1 - y)

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