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

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

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

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

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derivative of

y = 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 1 + t^{3} d t

n = 0 \sum \infty (- 1)^{n} (- 2)^{n}

\frac{2 s + 1}{( s + 1 ) ^{2}}

x \to - 2 lim (2 x^{2} - 8 x - 3)

\int \frac{9 x ^{2} - 8 x + 16}{x ^{3} + 4 x} d x

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