What is the derivative of x*e^{-x+1} ?

The derivative of x*e^{-x+1} is e^{-x+1}-e^{-x+1}x

What is the first derivative of x*e^{-x+1} ?

The first derivative of x*e^{-x+1} is e^{-x+1}-e^{-x+1}x

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derivative of

x \cdot e^{- x + 1}

e^{- x + 1} - e^{- x + 1} x

Solution steps

\frac{d}{d x} (x e^{- x + 1})

Apply the Product Rule:

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

f = x, g = e^{- x + 1}

= \frac{d x}{d x} e^{- x + 1} + \frac{d}{d x} (e^{- x + 1}) x

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

\frac{d}{d x} (e^{- x + 1}) = - e^{- x + 1}

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

Simplify

= e^{- x + 1} - e^{- x + 1} x

(4, - 4), (8, - 10)

\int \frac{3 + x}{3 - x} d x

x^{^{''}} + x^{^{'}} + 3 x = 0

\int \frac{8 x ^{3}}{x - 4} d x

\frac{x}{3 x + 5}

What is the derivative of x*e^{-x+1} ?
The derivative of x*e^{-x+1} is e^{-x+1}-e^{-x+1}x
What is the first derivative of x*e^{-x+1} ?
The first derivative of x*e^{-x+1} is e^{-x+1}-e^{-x+1}x