What is the derivative of y=2xe^{-kx} ?

The derivative of y=2xe^{-kx} is 2(e^{-kx}-ke^{-kx}x)

What is the first derivative of y=2xe^{-kx} ?

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

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derivative of

y = 2 x e^{- k x}

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

Solution steps

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

Take the constant out:

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

= 2 \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}

= 2 (\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}

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

Simplify

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

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