What is the derivative of axe^x ?

The derivative of axe^x is a(e^x+e^xx)

What is the first derivative of axe^x ?

The first derivative of axe^x is a(e^x+e^xx)

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

a (e^{x} + e^{x} x)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= a \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}

= a (\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}

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

Simplify

= a (e^{x} + e^{x} x)

What is the derivative of axe^x ?
The derivative of axe^x is a(e^x+e^xx)
What is the first derivative of axe^x ?
The first derivative of axe^x is a(e^x+e^xx)