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

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

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

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

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derivative of

y = 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

f (x) = x^{2} - 7

41 (6 t^{3} - 7)^{\frac{6}{5}}

\int_{0}^{\frac{π}{2}} t sin (2 t) d t

y = arctan (2 x)

cos (θ), sin (2 θ)

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