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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

e^{x} (1 + x) + 1 \cdot e^{x} : e^{x} x + 2 e^{x}

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

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