What is the derivative of xe^{x-1} ?

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

What is the first derivative of xe^{x-1} ?

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

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derivative of

x 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

\int e^{7 x} d x

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

f (x) = 13 x

f (x) = 10 x, at x = 10

y = - x^{2} + 5 x + 2, y = 2

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