What is the derivative of x*e^x ?

The derivative of x*e^x is e^x+e^xx

What is the first derivative of x*e^x ?

The first derivative of x*e^x is e^x+e^xx

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derivative of

x \cdot e^{x}

e^{x} + e^{x} x

Solution steps

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

Apply the Product Rule:

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

f = x, g = e^{x}

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

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

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

= 1 \cdot e^{x} + e^{x} x

Simplify

= e^{x} + e^{x} x

What is the derivative of x*e^x ?
The derivative of x*e^x is e^x+e^xx
What is the first derivative of x*e^x ?
The first derivative of x*e^x is e^x+e^xx