What is the derivative of x^5e^{2x} ?

The derivative of x^5e^{2x} is 5x^4e^{2x}+e^{2x}*2x^5

What is the first derivative of x^5e^{2x} ?

The first derivative of x^5e^{2x} is 5x^4e^{2x}+e^{2x}*2x^5

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derivative of

x^{5} e^{2 x}

5 x^{4} e^{2 x} + e^{2 x} \cdot 2 x^{5}

Solution steps

\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}

= \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

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

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