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

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

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

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

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derivative of

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