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Popular >

derivative of 2x^3e^{2x}

Solution

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

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \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}

= 2 (\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

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

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Frequently Asked Questions (FAQ)

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