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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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