What is the derivative of xe^{-7x} ?

The derivative of xe^{-7x} is e^{-7x}-7e^{-7x}x

What is the first derivative of xe^{-7x} ?

The first derivative of xe^{-7x} is e^{-7x}-7e^{-7x}x

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\frac{d}{d x} (x e^{- 7 x})

e^{- 7 x} - 7 e^{- 7 x} x

Solution steps

\frac{d}{d x} (x e^{- 7 x})

Apply the Product Rule:

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

f = x, g = e^{- 7 x}

= \frac{d x}{d x} e^{- 7 x} + \frac{d}{d x} (e^{- 7 x}) x

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

\frac{d}{d x} (e^{- 7 x}) = - 7 e^{- 7 x}

= 1 \cdot e^{- 7 x} + (- 7 e^{- 7 x}) x

Simplify

= e^{- 7 x} - 7 e^{- 7 x} x

f (x) = [(4 x^{2} + 3 x) cos (x)]

\frac{( 4 z + 4 )}{3 z ^{2} + 3 z + 3}

\frac{d y}{d x} = \frac{x y}{x ^{2} + 4}, y (0) = 6

10, x, \frac{x ^{2}}{40}

\int 2 cos (- 4 x) + 1 d x

What is the derivative of xe^{-7x} ?
The derivative of xe^{-7x} is e^{-7x}-7e^{-7x}x
What is the first derivative of xe^{-7x} ?
The first derivative of xe^{-7x} is e^{-7x}-7e^{-7x}x