What is the derivative of xe^{3x} ?

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

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

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

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derivative of

x 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

\int_{0}^{1} x 4 - x^{2} d x

\int (x^{2} + 3 x - 1)^{4} (2 x + 3) d x

f (x) = 5 csc^{4} (x)

1000 (1 + \frac{r}{12})^{60}

n = 1 \sum \infty \frac{1}{2}

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