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

The derivative of xe^{-bx} is e^{-bx}-be^{-bx}x

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

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

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

e^{- b x} - b e^{- b x} x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

= e^{- b x} - b e^{- b x} x

\int (5 t^{2} + 3 t) d t

\frac{d}{d x} (sec (x))

6 x + 7, x, 0, 8

\int \frac{1}{( 4 x ^{2} - 9 ) ^{3}} d x

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