What is the derivative of (2-xe^x) ?

The derivative of (2-xe^x) is e^x-e^xx

What is the first derivative of (2-xe^x) ?

The first derivative of (2-xe^x) is e^x-e^xx

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\frac{d}{d x} ((2 - x) e^{x})

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

Solution steps

\frac{d}{d x} ((2 - x) e^{x})

Apply the Product Rule:

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

f = 2 - x, g = e^{x}

= \frac{d}{d x} (2 - x) e^{x} + \frac{d}{d x} (e^{x}) (2 - x)

\frac{d}{d x} (2 - x) = - 1

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

= (- 1) e^{x} + e^{x} (2 - x)

Simplify

(- 1) e^{x} + e^{x} (2 - x) : e^{x} - e^{x} x

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

What is the derivative of (2-xe^x) ?
The derivative of (2-xe^x) is e^x-e^xx
What is the first derivative of (2-xe^x) ?
The first derivative of (2-xe^x) is e^x-e^xx