What is the derivative of xe^{x+1} ?

The derivative of xe^{x+1} is e^{x+1}+e^{x+1}x

What is the first derivative of xe^{x+1} ?

The first derivative of xe^{x+1} is e^{x+1}+e^{x+1}x

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

e^{x + 1} + e^{x + 1} x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

(2 + x) \frac{d y}{d x} = 3 y

\int_{0}^{2} 2 t^{3} d t

\frac{d}{d x} (x + y) = 2

8 t^{2} + 9

\int x^{2} e^{1 x} d x

What is the derivative of xe^{x+1} ?
The derivative of xe^{x+1} is e^{x+1}+e^{x+1}x
What is the first derivative of xe^{x+1} ?
The first derivative of xe^{x+1} is e^{x+1}+e^{x+1}x