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Popular >

derivative of 3x^5e^{2x}

Solution

\frac{d}{d x} (3 x^{5} e^{2 x})

Solution

3 (5 x^{4} e^{2 x} + e^{2 x} \cdot 2 x^{5})

Solution steps

\frac{d}{d x} (3 x^{5} e^{2 x})

Take the constant out:

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

= 3 \frac{d}{d x} (x^{5} e^{2 x})

Apply the Product Rule:

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

f = x^{5}, g = e^{2 x}

= 3 (\frac{d}{d x} (x^{5}) e^{2 x} + \frac{d}{d x} (e^{2 x}) x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 3 (5 x^{4} e^{2 x} + e^{2 x} \cdot 2 x^{5})

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Frequently Asked Questions (FAQ)

What is the derivative of 3x^5e^{2x} ?
The derivative of 3x^5e^{2x} is 3(5x^4e^{2x}+e^{2x}*2x^5)
What is the first derivative of 3x^5e^{2x} ?
The first derivative of 3x^5e^{2x} is 3(5x^4e^{2x}+e^{2x}*2x^5)