What is the derivative of (x-1e^x) ?

The derivative of (x-1e^x) is e^xx

What is the first derivative of (x-1e^x) ?

The first derivative of (x-1e^x) is e^xx

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

e^{x} x

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x - 1) = 1

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

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

Simplify

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

= e^{x} x

What is the derivative of (x-1e^x) ?
The derivative of (x-1e^x) is e^xx
What is the first derivative of (x-1e^x) ?
The first derivative of (x-1e^x) is e^xx