What is the derivative of xe^{-kx} ?

The derivative of xe^{-kx} is e^{-kx}-ke^{-kx}x

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

The first derivative of xe^{-kx} is e^{-kx}-ke^{-kx}x

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

e^{- k x} - k e^{- k x} x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

= e^{- k x} - k e^{- k x} x

\int_{1}^{\infty} 5^{- x} d x

x \to 1 lim (e^{6 x^{3} - 6 x})

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

x^{2} - x - 2, 3

x \to - 10 lim (2 x - 10)

What is the derivative of xe^{-kx} ?
The derivative of xe^{-kx} is e^{-kx}-ke^{-kx}x
What is the first derivative of xe^{-kx} ?
The first derivative of xe^{-kx} is e^{-kx}-ke^{-kx}x