What is the derivative of-2e^{-x}x ?

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

What is the first derivative of-2e^{-x}x ?

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

sin (4 x)

\frac{\partial}{\partial x} (\frac{1}{3 x})

x \to 1 + lim ((x - 1) ∣ x - 1 ∣)

\int cos (π) x d x

\int t^{17} e^{- t^{18}} d t

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