What is the derivative of x*e^{3x} ?

The derivative of x*e^{3x} is e^{3x}+3e^{3x}x

What is the first derivative of x*e^{3x} ?

The first derivative of x*e^{3x} is e^{3x}+3e^{3x}x

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\frac{d}{d x} (x \cdot e^{3 x})

e^{3 x} + 3 e^{3 x} x

Solution steps

\frac{d}{d x} (x e^{3 x})

Apply the Product Rule:

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

f = x, g = e^{3 x}

= \frac{d x}{d x} e^{3 x} + \frac{d}{d x} (e^{3 x}) x

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

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

= 1 \cdot e^{3 x} + e^{3 x} \cdot 3 x

Simplify

= e^{3 x} + 3 e^{3 x} x

What is the derivative of x*e^{3x} ?
The derivative of x*e^{3x} is e^{3x}+3e^{3x}x
What is the first derivative of x*e^{3x} ?
The first derivative of x*e^{3x} is e^{3x}+3e^{3x}x