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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial z} (ln (\frac{x y}{z}))

y = x^{2}, x = \frac{y}{2}

t \to 0 lim (3 e^{2 t})

\int - 2 sin^{2} (x) d x

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