What is the derivative of xe^x ?

The derivative of xe^x is e^x+e^xx

What is the first derivative of xe^x ?

The first derivative of xe^x is e^x+e^xx

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derivative of

x e^{x}

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = e^{x}

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

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

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

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

Simplify

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

y = x^{- \frac{2}{3}}

f (x) = e^{x}

f (x) = x, at x = 1

y = 2^{x}

x = 1