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}

20 e^{- x}

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

\int (\frac{ln ( x )}{x ^{3}}) d x

\int_{0}^{1} \frac{x}{e ^{x}} d x

\frac{d x}{d t} = x^{2} + \frac{1}{49}

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