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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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