What is the derivative of 4xe^{-x} ?

The derivative of 4xe^{-x} is 4(e^{-x}-e^{-x}x)

What is the first derivative of 4xe^{-x} ?

The first derivative of 4xe^{-x} is 4(e^{-x}-e^{-x}x)

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derivative of

4 x e^{- x}

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

Solution steps

\frac{d}{d x} (4 x e^{- x})

Take the constant out:

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

= 4 \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}

= 4 (\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}

= 4 (1 \cdot e^{- x} + (- e^{- x}) x)

Simplify

= 4 (e^{- x} - e^{- x} x)

\int \frac{x ^{3} - 3 x + 1}{y + y} d x

\int (4 e^{- 0.8 x}) d x

\frac{d x}{d t} = e^{- k t}

x^{2}, x^{3}

\frac{\partial}{\partial y} ((x^{2} + y^{2})^{\frac{3}{2}})

What is the derivative of 4xe^{-x} ?
The derivative of 4xe^{-x} is 4(e^{-x}-e^{-x}x)
What is the first derivative of 4xe^{-x} ?
The first derivative of 4xe^{-x} is 4(e^{-x}-e^{-x}x)