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

The derivative of x*e^x+e^x is e^xx+2e^x

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

The first derivative of x*e^x+e^x is e^xx+2e^x

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

e^{x} x + 2 e^{x}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

= e^{x} x + 2 e^{x}

What is the derivative of x*e^x+e^x ?
The derivative of x*e^x+e^x is e^xx+2e^x
What is the first derivative of x*e^x+e^x ?
The first derivative of x*e^x+e^x is e^xx+2e^x