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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\frac{\partial}{\partial x} (4 y + 9 x^{2})

\frac{d y}{d x} = 17 x + y - 17

\frac{d}{d x} (x^{(\frac{1}{2})})

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

\frac{1}{( 1 - x ^{2} )}

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