What is the derivative of x^5e^{4x} ?

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

What is the first derivative of x^5e^{4x} ?

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = x^{5}, g = e^{4 x}

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

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

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

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

9000 e^{0.08 x} (- 0.08)

\frac{d}{d x} ((5 x - 1)^{3} (x^{2} + 1)^{5})

f (x) = 8 - 2 x^{2}, at x = 0

\int x 2 x + 5 d x

f (x) = 25 x^{\frac{4}{5}}

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