What is the derivative of x^4e^{8x} ?

The derivative of x^4e^{8x} is 4x^3e^{8x}+e^{8x}*8x^4

What is the first derivative of x^4e^{8x} ?

The first derivative of x^4e^{8x} is 4x^3e^{8x}+e^{8x}*8x^4

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\frac{d}{d x} (x^{4} e^{8 x})

4 x^{3} e^{8 x} + e^{8 x} \cdot 8 x^{4}

Solution steps

\frac{d}{d x} (x^{4} e^{8 x})

Apply the Product Rule:

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

f = x^{4}, g = e^{8 x}

= \frac{d}{d x} (x^{4}) e^{8 x} + \frac{d}{d x} (e^{8 x}) x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (e^{8 x}) = e^{8 x} \cdot 8

= 4 x^{3} e^{8 x} + e^{8 x} \cdot 8 x^{4}

\frac{d}{d x} (I n (x^{2} + 1))

\frac{\partial}{\partial z} (2 x z^{2})

x \to \infty lim (x^{a})

y = 2 x - 2 x^{2}, at x = - 1.5

y = (x + 1)^{x^{2}}, (0, 1)

What is the derivative of x^4e^{8x} ?
The derivative of x^4e^{8x} is 4x^3e^{8x}+e^{8x}*8x^4
What is the first derivative of x^4e^{8x} ?
The first derivative of x^4e^{8x} is 4x^3e^{8x}+e^{8x}*8x^4