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

The derivative of (x+1)e^x is e^xx+2e^x

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

The first derivative of (x+1)e^x is e^xx+2e^x

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derivative of

(x + 1) e^{x}

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

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

What is the derivative of (x+1)e^x ?
The derivative of (x+1)e^x is e^xx+2e^x
What is the first derivative of (x+1)e^x ?
The first derivative of (x+1)e^x is e^xx+2e^x