What is the derivative of x^4e^{2x} ?

The derivative of x^4e^{2x} is 4x^3e^{2x}+e^{2x}*2x^4

What is the first derivative of x^4e^{2x} ?

The first derivative of x^4e^{2x} is 4x^3e^{2x}+e^{2x}*2x^4

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\frac{d}{d x} (x^{4} e^{2 x})

4 x^{3} e^{2 x} + e^{2 x} \cdot 2 x^{4}

Solution steps

\frac{d}{d x} (x^{4} e^{2 x})

Apply the Product Rule:

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

f = x^{4}, g = e^{2 x}

= \frac{d}{d x} (x^{4}) e^{2 x} + \frac{d}{d x} (e^{2 x}) x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= 4 x^{3} e^{2 x} + e^{2 x} \cdot 2 x^{4}

What is the derivative of x^4e^{2x} ?
The derivative of x^4e^{2x} is 4x^3e^{2x}+e^{2x}*2x^4
What is the first derivative of x^4e^{2x} ?
The first derivative of x^4e^{2x} is 4x^3e^{2x}+e^{2x}*2x^4