What is the derivative of x^2e^{3x} ?

The derivative of x^2e^{3x} is 2xe^{3x}+e^{3x}*3x^2

What is the first derivative of x^2e^{3x} ?

The first derivative of x^2e^{3x} is 2xe^{3x}+e^{3x}*3x^2

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derivative

2 x e^{3 x} + e^{3 x} \cdot 3 x^{2}

Solution steps

\frac{d}{d x} (x^{2} e^{3 x})

Apply the Product Rule:

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

f = x^{2}, g = e^{3 x}

= \frac{d}{d x} (x^{2}) e^{3 x} + \frac{d}{d x} (e^{3 x}) x^{2}

\frac{d}{d x} (x^{2}) = 2 x

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

= 2 x e^{3 x} + e^{3 x} \cdot 3 x^{2}

What is the derivative of x^2e^{3x} ?
The derivative of x^2e^{3x} is 2xe^{3x}+e^{3x}*3x^2
What is the first derivative of x^2e^{3x} ?
The first derivative of x^2e^{3x} is 2xe^{3x}+e^{3x}*3x^2